Are tangent to each other if they are tangent to the same line at the same point.
A tangent to a circle is a line, coplanar with circle, that intersects the circle in exactly one point. The point is called the point of tangency. In the figure below, point P is the point of tangency. A common tangent is a line that is tangent to each of two coplanar circles. A common tangent can be tangent either internally or externally. A common internal tangent is a common tangent that intersects the segment that joins the center of the two circles. Three congruent, coplanar circles overlapso that each center lies on the other two circles. The diameter of each circle is 8 centimeters. What is the area of the triangle formed ny connecting the centers of the circles? Express your answer in simplest radical form.  Coplanar means on the same plane. For example, if a laser gun shot straight through the center of both circles, then unless they both have the same center, it wouldn't jus … t pierce the two circles, but would slice them clean in half. Concentric circles have the same centre, therefore, if they were the same circles with the same radius, … then they would all lie on top of each other and be effectively one circle. Answer by BugQ. Confidence votes 44. Coplanar means on the same plane. For example, if a laser gun shot straight through the center of both circles, then unless they both have the same center, it wouldn't just pierce the two circles, but would slice them clean in half. In simple terms, the definition of plane is a flat surface. Coplanar means on the same plane, so we can imagine that non coplanar means not on the same plane. For example, if you draw a square and point on a piece of paper, the t … wo objects are coplanar. Definition of Coplanar Lines. Coplanar lines are lines that lie on the same plane. Picture a giant sheet of paper. Whatever lines are drawn on that sheet of paper will be coplanar because they are lying on the same plane, or the same flat surface. Look at this image.  Abstract. We define the lines associated with two coplanar circles, and give the distributions of any two coplanar circles and their associated lines. Further we prove that the distribution of two coplanar circles with no real intersection and their associated lines is a quasi-affine invariance. Then the results are applied to calibrating a camera. The calibration method has the advantages: (1) it is based on conic fitting; (2) it does not need any matching. (e). The separate case. C 1, C 2 intersect at two different pairs of conjugate complex, the two associated lines are a line such that the two circles lie on the different side of it, and the line at infinity such that the two circles lie on the same side of it. Proposition 2 will prove this. Two coplanar circles are tangent to each other if they are tangent to the same line at the same point. Tangent circles may be tangent either internally or externally. Tangent circles are tangent internally if one lies in the interior of the other (except for the point of tangency). In the figure below, point P is the point of tangency. A common tangent is a line that is tangent to each of two coplanar circles. A common tangent can be tangent either internally or externally. A common internal tangent is a common tangent that intersects the segment that joins the center of the two circles. In Section 3, the lines associated with two coplanar circles are defined, and the distributions of the two circles and their associated lines are investigated, and further a quasi-affine invariance of two coplanar circles with no real intersection is proved. (e). The separate case. C 1, C 2 intersect at two different pairs of conjugate complex, the two associated lines are a line such that the two circles lie on the different side of it, and the line at infinity such that the two circles lie on the same side of it. Proposition 2 will prove this.
http://jwilson.coe.uga.edu/EMAT6680Fa05/Parveen/ASSIGNMENT%206/Assignment%206.htm http://www.chegg.com/homework-help/questions-and-answers/three-congruent-coplanar-circles-overlapso-center-lies-two-circles-diameter-circle-8-centi-q1668517 http://www.answers.com/Q/When_are_two_coplanar_circles_concentric http://www.answers.com/Q/What_are_coplanar_circles http://study.com/academy/lesson/coplanar-lines-in-geometry-definition-lesson-quiz.html http://www.sciencedirect.com/science/article/pii/S0262885605002064 http://jwilson.coe.uga.edu/EMAT6680Fa05/Parveen/ASSIGNMENT%206/Assignment%206.htm http://www.sciencedirect.com/science/article/pii/S0262885605002064
what are coplanar circles