## Task 3 - 040923

Given are three different points that do not lie on a straight line. A circle is to be constructed around each of these points such that these circles touch each other externally in pairs.
The three points are denoted by $A, B$, and $C$ and are considered as the vertices of a triangle with sides $a, b, c$. The radii of the three circles around $A, B$, and $C$ are (in this order) $x, y$, and $z$. Then it holds that:

$$
x+y=c ; \quad y+z=a ; \quad z+x=b
$$

From this, it follows that:

$$
x=\frac{-a+b+c}{2} ; \quad y=\frac{a-b+c}{2} ; \quad z=\frac{a+b-c}{2}
$$