(I) The centers of the sought circles lie either (1) on the circle around $M$ with the radius of length $r+r_{1}$ or (1') on the circle around $M$ with the radius of length $r-r_{1}$, since they are supposed to touch $k$, and (2) on the circle around $M_{1}$ with the radius of length $r+r_{1}$, since they are supposed to touch $k_{1}$ and have the same radius as $k_{1}$.

(II) Therefore, the centers of the sought circles result from the intersection points of the circles according to (1) and (2) (these are 2 intersection points) and as the point of tangency of the circles according to (1') and (2).

This point lies on the line connecting $M$ and $M_{1}$. The points of tangency of the circles are obtained by connecting the centers of the touching circles. There are exactly 3 circles that satisfy the conditions of the problem. The proof follows from (I).
## Task 2 - 070822

Given are a circle $k$ (center $M$, radius of length $r=6 \mathrm{~cm}$) and a circle $k_{1}$ (center $M_{1}$, radius of length $r_{1}=2 \mathrm{~cm}$). Both circles touch each other externally.

Construct all circles with a radius of length $2 \mathrm{~cm}$ that touch the two given circles!

Also construct the points of contact of the sought circles with the given ones!