Hello and welcome to the CMC markets non-compare roles webinar with me Dave Madden Today's date is Friday the 7th of December 2018 and the time has just gone 1315 GMT quarter past 1 p.m. P.m. UK time before we actually kick off the non-compare Webinar, I just want to leave these risk warnings on the screen here in front of you It's all very straightforward it essentially states Anything that is covered in this webinar is purely just my own comments and opinions and views And it should not be taken as explicit training or investing advice It's all very straightforward. So I know a lot of you have been to our webinars before So, you know the drill whereby we discuss what's going on ahead of in terms of in terms of the news The news today the big topic you'd be watching out for the state of the US economy and then we'll probably have is I'd have passed The life numbers will come out we'll discuss those and then we'll also look at market reaction in relation to what's going on So, thank you for bearing with me on that front Essentially we have we have a work we have a lot of on payrolls reports coming out now in about 13 minutes time It's kind of this concept even as past one we're expecting hope the writers were expecting 200,000 jobs to be added to the payrolls For the month of November Just taking a look here at the Up there on a road is terminal. I hope you can see that. Okay Yes, just let you know as anybody who is having issues with the sound Please feel free to let me know more than happy to tell about on that front but in relation to in relation to Expectations we are expecting 200,000 jobs to be added for the November report keep mine That would be a decline in the rate of jobs growth if the person with the October report Which came in at 250,000 on the average on the unemployment front We're expecting the unemployment rate to hold steady at 3.7 percent Unshaded in the previous month and on the average earnings front We're sending average earnings on a yearly basis to increase by two three point one percent That'll be the same growth rate we saw in October and on the earnings front on a monthly basis we're expecting Give me we're expecting average earnings to increase by zero point three percent of an improvement on the zero point two percent That was achieved In October now to be perfectly honest if the US Academy keeps adding that there they're about 200,000 jobs every single month That's enough to keep the US Academy keep jogging along unemployment rate is a as a multi-decade lows in the US We're talking, you know, we're talking only three point seven percent on unemployment We're essentially at full employment a tick up a movement of say one tenth of one percent in either direction Obviously lower is better, but even if it does have a slight no job It isn't the end of the world. It's only if you have numbers that you know, you know some 100,000 Jobs are added or even even jobs declined and payrolls Or else we had you know, she's you know a sizable increase of say zero point three percent Whatever 0.4 percent in the unemployment rate when they were actually starting to get worried the US job market is in a very very stable position Uh, for me, it's all about the job. It's all about the earnings figures Um, but US workers earn more they tend to spend more. Uh, so if we can see Growth rates of say three point one percent or more on an annual basis or you know, take take me up on a month on month basis For me, uh, that's actually that's actually probably the most important thing within this payroll Obviously a clean sweep and a really good really impressive set of numbers would have You would have the unemployment rate top in 200,000 Do you would have either no revisions or the very least positive revisions to the old number of 200,000 The unemployment rate would either hold steady or even actually decrease and you have solid Solid figures on the earnings front. Now the classic example What you see in non farm payrolls is traders and the financial markets often spend too much time Being fixated on the headline number and the author could determine The the entire report just on whether the headline figure was exceeded or whether it was not exceeded Quite a few times over the years. I've seen the case where The headline number for example was actually worse than expected But then which then when traders looked at the other details The found out that the previous month's number was revised higher and then unemployment may have dropped and wages Would have been strong or conversely. There's been occasions where the headline figure topped expectations The markets moved in the direction which would which would be which would welcome Higher a stronger jobs market But there was there was downward revisions to the old month's number Unemployment ticked up or the wages were recovered expected So in my view the report needs to be taken as a whole. You can't just kind of bet that You can't just place a trade solely around or take or take A snapshot of us economy solely on one number for me. It's it's a kind of a it's a mixture of the whole lot And you know in recent months or even in the last year year and a half I would say that the earliest component is the most important component a number of years ago four or five years ago It was actually you needed more jobs to be created But now we're at such levels That it's almost it's almost Um, it's it's it's it's become less important. It's not irrelevant. Of course it's relevant but it's it's become less important and Even though the correlation hasn't been great between the non-farm payrolls and the adp figures and the jobless claims If you look at the adp figures Which were up yesterday, um, it came, you know, it came in below expectations But they still added some like 179,000 private sector jobs throughout 2018 the adp employment has been about An average or probably an average above 200,000 jobs per month. Once again, it's not a perfect correlation In fact, the correlation isn't great in terms of month by month But the wider view of the non-farm payrolls report is showing regularly showing Averaging of 200,000 jobs a month and then we see we're seeing the seminar with the adp employment and On the early on the jobless claims front in the u.s. Um, most important most recent reading yesterday's reading auto jobless claims ticked up Ticked up I came in at 231,000 Which pretty is a bit off the recent lows because the recent lows was 200 1,000 But then again that figure was the lowest level in nearly 49 years So even though the jobless rate in the United States has ticked up as a small bit It's still in the grand scheme of things, you know, not too far away from the lowest levels in In several decades, so Things looking quite good on that front. Um, if you take a look at yesterday What we had out yesterday was one the economic indicators yesterday was the ism Was the ism figure It should be found on our market on our On our calendar and if you throw the calendar can be found under a market pulse And then go through the fourth option down. Take a look yesterday And um, we can see the ism manufacturing figures here the is and if you look at the ism non-manufacturing survey The um, the overall figure um came is uh 64 point 60 64.3 was a big improvement on the 61.7 That was recorded, but within that we can see new orders and we can see the employment index and we can Employ and the employment component tick lower. So yesterday we had a slight tick lower and the employment component The jobless claims actually slightly ticked down slightly, but it's still well after most of our recent months The issue and the adp figures came in a little less than expected so As I was saying sometimes There isn't a whole lot of strong correlation Which probably leaves it easy to believe you could see a number except in the in excess of 2000 for today's non-vampirals figure broadly speaking Uh, the u.s economy hasn't has been has been in decent shape Some of the economic indicators haven't been as strong As others recently, but by and large the u.s economy is in very decent shape What is important though? Um is the Fed of reserve the Fed of reserve are still about six markets of pricing at about a 60 60% chance of the of a rate hike Um later this month, but that's a big drop off. Um, consider what it was at Only only a matter of weeks ago Only matter months ago. There was a very there was there was talk of a definite rate hike in december and possibly two If not three rate hikes in 2019 that was the the the general view of the market Let's get going back in early october When jaron pal the head of federal reserve stated That the interest rate in the united states was nowhere near was still very far off or a very long way off from the neutral rate Since then, um, mr. Powell has actually rolled back on that And he recently stated that a couple of policy makers at the third field that interest rates in the u.s Are pretty much very pretty close to the neutral rate. Um Also, what we've seen here one which was how this has impacted the financial markets is um, is u.s Government bond yields this year is the yield on the 10 year u.s government bond as we can see it's been pointing lower This is most in early november right up until early december's the last month We can see that the yield on the u.s 10 year yield has declined From in from in around the kind of 3.2 three spot three spot two three down to two spot eight nine and even the recent low was a 2.89 spot Two spot eight nine one seven so what that tells us is that The decline in the yield on the 10 year government bond suggests that traders are less fearful or Traders are pricing in fewer rate hikes in the near term So when it was on the yield was up over 3.2 percent That was that was during the kind of era about a month ago when traders were thinking We could have a rate hike in deck and we could have two if for three rate hikes in 2019 Now with a scenario whereby deck is only about a 60% probability and going into 2019 We could see you know a far far fewer number of rate hikes in that so When bond yields are pushing lower that's when traders get worried thinking hold on Maybe the u.s economy isn't isn't and it's going to shape as in the she thought because there are fewer rate hikes on the agenda If you take a look down here and we see the yield on the two-year note The you can yield on the two-year note is 2.7 say in in the region of 2.77 2.68 In this region here if you scroll down to the five-year yield The yield on the five year is 2.75 Uh versus 2.75 so the yield on the five-year note is below that of the two year of the two year That is actually itself in a bit of a worry because when the longer for the yield on the longer data bond starts Is below that of the shorter data bonds That is that's that's a that's a often the the bottom market telling us that they expect The number of rate hikes and the kind of medium term to be kind of far fewer in the current position and when you have a scenario whereby the yield on say the 10-year yield which is currently 2.89 and that was to drop below the The the two years which is currently in the region around 2.77 Should we have a should the 10-year drop below the two-year that would be of course scary just because When that has happened in recent in recent decades that is always kind of being a forewarning to a recession in the u.s economy so I think it's a bit overdone because I think the u.s In u.s economy is in decent shape But it's almost like it's almost the way to finish talking about it now It's almost like a bit of a self-definition prophecy whereby a bond year the two-year bond yield drops below that of the two-year The 10-year bond yield drops below that of the two-year bond yield That will get traders talking about a recession and lo and behold If traders has a After lo and behold if traders are to act at this recession They could then actually alter their spending which may may actually bring about a decline in economic activity which could which could in theory need to Negative growth and in turn a recession. So we are at 129. The numbers will be coming up now In a few minutes time I'll just take a look as I was saying we take a look here on The chart of economic indicators We get the exact countdown here on On the Reuters terminal, which I have here So it's less than nine seconds. So this is The main figure to keep enough for it'll populate in this box here That is a big miss The non-framperous figure came in at 155,000 so well below The consensus estimate of 200,000 also adding to that That that is in relation to Canada So the headline pick came in at 155 Notice how there's a negative revision that the old number of 250,000 for October was revised lower to 237 So that's a double negative Unemployment health steady at 3.7% in line with expectations The average earnings at a year-on-year basis health steady at 3.1% in line with expectations. That's good What's a bit worrying here is the average earnings on a monthly basis health steady at 0.2% but That came in below expectations at 0.3% and on top of that We can see that the the previous monthly number was revised from 0.2% to 0.1% So my guess is my overall take this isn't okay An okay jobs report The headline figure was poor. There's a there's a negative provision to the previous number And on top of that The the one of the earnings component was was wasn't too wasn't too hot Uh, because the average earnings on a monthly basis health steady But the previous most number was revised lower. So a bit weaker on the earnings now what I've just done there is Added 155 and 237 together and divided by 2 that comes in a few after average of two months reports together um You get a reading of 200 and 196,000 jobs So this report on its own is a weak number, but the previous number despite the making revision is still positive So I think what's being a common theme in the last few months is actually lumping two reports together the current one and the uh, and their own and the other revision to the old one Uh, so I think actually it's still looking okay at the u.s. jobs market all of them is is that uh, is a 3.7% and on top of that the actual head the On average to the average s us is as is You know adding about on average 200,000 jobs per month. So things are looking so we get pretty good that being said um I think I suspect there's going to be a bit negative in terms of the move of the u.s. dollar and we could see a bit of a lift to the um to the Uh to the upside in terms of the equity markets while we're here We also talk about the canadian numbers. Don't forget the uh the dollar category in play Canadian unemployment, uh dropped to five point six percent better than expected and also what what's impressive about these numbers is that um in terms of full-time employment Full-time employment increased And also the employment change was 94,000 Which is completely smashed the 11,000 that markets very expected that markets were expecting and what's good about this is that of the 94,000 We saw that nearly 90,000 came in full-time employment and only only a small amount only 4,000 came in prior time employment So actually very very impressive numbers out of Canada the headline rate fell We just very strong employment change and the vast majority of the employment change came from full-time work That's a very strong number out of Canada. So that would start off the uh taking look at what's going on with the dollar card I suspect we're going to be much lower on the dollar card um on the back of those numbers We've seen it out of both countries. So Take a look now What i'm going to do now is uh now that we've anybody wants to kind of share any comments on their thoughts or opinions on the numbers Feel free to do so and over the next, you know 12 to 15 minutes I'm going to run through some popular markets. So I think they're worth having a look at But if there are any markets you guys want to have a look at feel free to um Feel free to type in the chat box and I'll take a look at those markets I'll be covering the usual stuff the big indices the big currencies uh and the commodities What will I say to you folks? Uh, we had a weak weakish or middle of the road Set of figures from the US and a very strong set of numbers from the uh from the uh from Canada I want to know and a fairly sizable sell-off in the in the dollar card Excuse me That being said, uh, we have even though we've had had a pullback. I think that needs to be taken That needs to be taken um in in the context of the wider view Bearing in mind yesterday the dollar card Had a level not seen Since june 2017 so we're talking a bit. We're essentially at yes as of yesterday an 18 month high on dollar card So a bit of so the market is doing well classic example of higher highs and higher lows along here Uh, so this could be an opportunity for some potential buying should you see further crown loss on the dollar card? Yes, you could see some potential buying into this market Just because the market's in a classic example of an upward trend has been the way since this is early this is early october Buying on the dip has been a popular strategy recently some might be an opportunity for some traders actually to look Um, I've been I've been opportunity to look Uh, look into uh, we could see some buyers and um buy into dollar card Given that buying the dip has been a popular strategy recently If we do see further pressure on these numbers, we could see the the dollar card head back down towards the 132 50 area Notice how there was a bit of that has been a fair bit of consolidation both um Resistance and support from the very recently and a move below that might bring the recent early december nose of the 131 60 region into play Should you move to the upside? And if you take out the uh, the recent high we could be heading up towards the 135 region on dollar card Um, are there any other markets? Um I was asked the question about what platform do you use to show those graphs and figures one of the So this platform we've shown you is actually our actual Economic calendar which can be found on our website under market pulse go to the the fourth option down the other Um chart that I was showing you on the block of economic data. I've shown you was actually the lowest of terminal that I actually have Uh, as a part of my job as a market analyst and lowest terminals are fairly expensive So it but it's it's a If you're going to be a market analyst, I'm looking for a a broken company a trading company It's sort of a a necessary expense You can you can look into a lot of trouble yourself, but uh, you find that they're fairly expensive Um, are there other markets you'd like me to uh to have a look at? What I'm going to do now is take a look at the s and p 500 So what I will be doing is even if he makes the s internet, I'll be taking a look at a couple of the um A couple of the uh the major indices currencies and commodities at the back of this and like I said to you I thought it was a Slightly weakish number and what have you seen here? We see the spike higher on the s and p 500 to the market is pushing higher The long the short of it is this These numbers in my opinion, I think what will will Temper the Fed and reserve in terms of their language and the willingness to hike rates over the next six or take the 12 months And uh, we're we're seeing the play out so far in the s and p 500 futures If you take a look at the daily chart of the s and p 500 If you draw a line between the lows of february 2016 On november 2016 we get this trend line here and as you can see um, it's been It was well respected back in in late late october again In late november and granted it traded below it yesterday, but notice how it closed well well above it So you could you could you know, you still include that You can still you you can still leave that the trend line and touch on touch rather So essentially while we hold north of this trend lines, but all the kind of chaos That's going on global financial markets While we hope we hold north of this trend line on the s and p 500 It's likely we could see further gains being made from here Uh, should we should we look to push on higher from here? We could be looking heading up towards the recent high Which comes into play in around two thousand eight hundred and thirteen Notice how the high here was just shy of the high in that early november which was in around the two thousand eight hundred and seventeen So, uh, if you do see the market drifted that low We might see some fresh buyers enter the fold just because there's been a number of occasions where this trend line has active decent support Now if you are going to be trading, um, the s and p 500 It's also worth just at least keep an eye on what's going on with the dow Jones and Uh, dow theory, uh, one of the tenants of dow theory is that the indices or the averages must confirm each other So as I talked about how the s and p 500 is about currently above its trend line We can see here that the um That the dow Jones granted it has traded below its trend line a number of occasions But we are it is back above this trend line here If you draw a law between the lows of february march april and may you get this trend line here the dow Jones and What if you're going to trade the s and p 500 and while the dow Jones is above this trend line It makes it more likely that both markets are going to move higher If both markets fall below the respective trend lines It makes it more likely that the both markets will move lower If one is above this trend line, you know, the lowest trend line That's really a bit of indecision and the outcome or the potential outcome becomes less clear Um, like I said feel free. I'll be chatting here for another five or six minutes I'll take a look at a couple of currency pairs. Are there any is any markets? You want to have a look at just just feel free to Uh stick in the chat box. Don't be shy. I'll happily uh Trappley Online whenever workers you you put forward I'll just take a look at a very small chart a very short date of time As you can see here the euro rallied on the back of this largely because of the kind of middle of the road numbers that come out of the us This is this is an interesting one because Even though the united states appear to be less Um, hawkish than it once was and it's taking a slightly more double stance the euro is still under major pressure And and it's but but if you could kind of hold up hold above the lows here Um at 112 16 we could look to kind of push on higher and this blue line here the fifth day moving average Which comes into play around the kind of 140 one spot 14. Yes, I will do the next next. Um This this the fifth day moving average which comes to play at one spot 40 11 This could act as resistance because it's been a number of occasions We can see here that it acted as decent up resistance back in early october And if metric has acted as resistance in the past it makes it more likely it will just do so in the future And even if it goes beyond that even if it runs into the uh, you can't see a lot of resistance In this area here is this yellow line Uh, which comes to play just north of 115 10 and 115 10 is also a fairly important region For um euro dollar because uh over the over the summer months it did act Actors both really support and resistance in recent months. So 115 is also noted to keep you now for and if you do have a push on higher from 115 We could be looking at it heading up up towards one spot 17 50 this early here This red line here the two-day moving average But if the market does turn over itself and we take off the recent lows here in of november We then be looking at levels and head back down towards levels not seen Since june 2017 so 18 month lows a break below once spot 12 16 that'll be a pretty bearish sign for um for the Euro versus the u.s. Dollar I take a look now at the dollar index. Yes, I will come on to wti and Brent uh, given how choppy and crazy The oil markets have been in recent recent sessions Dollar index like I'll say we've seen the uh, we've seen the The euro and the and the canadian rise versus the the greenback on the back of this There's your answer right there folks numbers come on half one for any decent sell-off in the in the dollar in the dollar index granted some of it has been actually brought back into play but uh Ultimately the wider view is is still Uppertrained is still in in play for the uh for the dollar index, but what I will say is this is that We could be and I we could be at a point where the dollar index might be looking for another steam And I say that because the high here in november failed to take out Failed to take out the high um in early november Then the highs here Uh in late november failed to take out the mid november highs the highs in december failed to take out Failed to take out the november high so even though we haven't actually begun to get a print new kind of multi week lows yet um We haven't taken out new highs In order for the trend to be settled an upward trend that needs to be creating higher highs and higher lows Like what we were seeing Like what we're seeing here market goes up pulls back mark goes up pulls back up pulls back We have this hitting hitting the higher highs and given the given the talk of recession given the um What's going on? You know, it's coming far new years given today's numbers in terms of dollar farm perils I was I would say that that kind of adds up. We're not seeing higher highs for a reason other than on the dollar index now I'll thank you for that for the december 4th low at 96 spot 30 because a break below that that's that's most recent Kind of obvious big low a break below that could suggest We then be hitting kind of, you know Multi week lows and a break below that could bring the kind of mid november low at 95 spot 92 into play And that in itself, uh, would also would also be fairly bearish if you take off that level Okay, I have a time to look at a couple more markets. So look at wti and also look at brand crude oil So obviously The major commodities are listed in us dollar. So we can't a weakened A weakened, um us dollar It makes it commodities a bit more a bit more affordable. But then again, what's going on in the oil market is, uh, is, um In relation to opec and cuts is also a very important issue as well So as you can see here, all the market was creeping a bit higher before, um before the almost renounced they renounced here and The south u.s. dollar has managed to especially give a brand another assistance now uh, a big big fan of Looking at what the trend is doing and the market is in a classic example of a downward trend lower lows and lower highs all the way Along that being said We have seen a bit of a bottom forming in around here and if you can hold off of the recent lows And it depends on this candle Um, today is out We've had a very decent bullish candle here on the body of this candle Could be construed as a bullish engulfing here So we could look for the the body of this candle could basically fully engulf Yesterday's council. This is the potential to be a bullish engulfing And notice how the lows here are well above the recent lows and if you can hold above the recent lows This area here the 29th of November, which coming to play at a 57 spot 50 Hit around there if you could hold above the recent lows We could see the oil market pushed on higher bear bear in mind that keep an eye on what's going on with the opec Obviously, I've been doing a live webinar for the last half an hour or so any new announcements haven't I've been able to um, I've been able to spot The last I heard was that there is a cut in the pipeline You've heard the pun But it's kind of looking like the cut may not be as big as the market as traders were originally expecting Going into the meeting a few days ago people were talking about a cut of 1.4 million barrels of oil per day I've been here. I've been speaking to seeing on twitter and hearing the very different sources We could be looking at a cut of say there there about a million dollars in a barrel a million barrels of oil per day Um, I shouldn't that be the case that may not be enough because That may not be enough to actually stem this wider downward trend And also this upward move here that we're seeing could be just a bit of a short covering And I could apparently think in advance of the actual final announcement being made um for what I gather countries like Iran want to be Um, but not to be left exempt from any kind of across the board coordinated cut Um, Saudi Arabia aren't that bother Are looking to cut as deep as some traders originally assumed they were because the Saudis want to keep the Americans outside So as always with OPEC and uh, and it's partner russia They're not, you know, they come together as a group But they usually have their own agendas and the often and the often is really going to push forward their own agendas So there isn't this there isn't always Everyone is singing from the uh, it's the same hem sheet Bearing in mind like I said, if you think if you say if you say if you say above these lows I think we could squeeze up back up towards this area here In around six seven dollars a barrel maybe if you're towards going to 69 But but you can't really ignore the uh, the very strong downward trend that we've been in And of course if you take out the recent lows here that would would point to to further losses That's a very crude oil and I'll take a look at wti And then we look to uh to wrap things up Once again the five minute chart shows that we had a very decent move to the upside on the back of that On the back of the actual note the figures being released Very similar looking chart here on wti Class example of a downward trend lower lows and lower highs all the way downtown um similar situation here whereby If we hold above the recent lows uh wti which covered the play at 49 spot 29 hold above this area here We could see a bit of a squeeze higher. We could head back up towards 55 or not. There's a bit of consolidation in around here um In around the 57 spot 24 57 spot kind of 90 that that kind of area we could see a bit of a squeeze higher here Basically, we need to kind of really take at least take out this area here before we become more confident that the downward trend is going to come to an end and if you go beyond that 60 bucks to them in next year to keep an eye out for but If you take out these lows here, that'll be another another kind of low added to the uh, that'll be another multi-month low You know, it's it's october 17 is last time we start these levels. So we are talking, you know, you know 14 month low if you take out our recent low here, we could be looking back down towards 40 a dollars per barrel Um, I do want to I gotta wrap things up there because it's now coming up to 10 to 2 and I've been talking for uh For just over half an hour. I do it. Uh, thank you for for logging in on our trading platform Under uh insights we're gonna show you here if you want to replay this video There's going to be a link to this webinar under insights insights can be found on your market pulse And it is the second option down. Also, please feel free to contribute to our chart form section here Uh chart chart forward can be found on the market market pulse. It is the um, the third option down And essentially all you do is anybody with a kind of cmsc can kind of contribute to myself I've been around less often contribute for about you take a screenshot of a particular market And then just kind of write some commentary on on what you think the market's doing in terms of price action Uh, I do want to thank you for tuning in this week And if you've any of any comments you want to make in relation to any of the videos we've made here at cmsc markets Please feel free to review and do reviews and that's all for me this week. Thank you very much


This study examined the effects of intra-artifacts on deep learning-based sleep staging systems. The authors found that intra-artifacts can have a negative impact on the accuracy of the systems and proposed a new method called SOBWT which combines wavelet transform and second-order blind source separation to reduce the negative impact of intra-artifacts. This method was tested on three different datasets and showed improved accuracy when compared to other artifact reduction techniques. This article was authored by Hanyu Zhu, Yonglin Wu, Mingxian, and others.


Hi, I'm Zor. Welcome to Unizor Education. I will just present a very simple problem related to angles. It's a very short one and really very, very simple one. But it's just an introduction into a series of problems which might actually be much more complex than this. In any case, we always start with the simple thing and then we go to more complex. So here's the problem. Let's consider we have two supplementary angles. Supplementary means that together they form 180 degree angle. So this is my angle alpha and this is my angle 180 degrees minus alpha. So the problem is let's have two bisectors of these two angles. Bisector of this angle and bisector of supplementary angle. One angle will be A, O, B. Another will be B, O, C. And the bisectors they will call G and E. So what's given? Given that A, O, B and B, O, C are together 180 degrees. Okay, angle A, O, B plus angle of B, O, C equals 180 degrees. Now when I have angle plus angle it actually means measure of this angle. So excuse me if I don't put this measure off or something. What else is given? That O, G is bisecting the angle A, O, B, which means angle A, O, G. A, O, G is congruent to G, O, B. And this bisector is dividing the B, O, C in half. So the angle B, O, E is congruent to E, O, C. Okay, what should be proven? We're to prove that angle D, O, E, the one which is composed of two bisectors, measure of this angle is 90 degrees. So these are perpendicular to each other. Well, I spent so much time explaining the condition basically of this little problem. Solution is absolutely trivial. Let's think about it in the following way. The angle D, O, E, the one which we have to really calculate the value of, it's a sum of two angles, G, O, E and D, O, E. D, O, B plus B, O, E, which in turn equal to, if this angle measures as alpha, and this measures as 180 degree minus alpha. So half of this, since O, D is bisecting, so half of this will be one half of alpha plus one half of 180 degree minus alpha, which is equal to, well, if you will open this parenthesis, you will have one half alpha plus one half of 180, which is 90 degree, and minus one half alpha, which is equal to 90 degree. So that's the proof. Very easy. And I don't want you to be very excited about this particular problem if you solve it yourself. There is absolutely nothing to it. It's a very easy one. But anyway, as I was saying, it's always the simple problems which will fade the road to more complex ones. So thanks very much, and good luck in other problems.