2. The radius of the circle inscribed in the triangle is 2. One of the sides of the triangle is divided by the point of tangency into segments equal to 6 and 14. Find the other sides of the triangle.

Answer. 7 and 15.
Let K, L, M be the points of tangency of the inscribed circle with the sides AB, BC, AC of triangle $ABC$ respectively; thus, $AK=6, BK=14$. By the property of the equality of tangent segments drawn from a point to a circle, we get $\mathrm{BL}=14, \mathrm{AM}=6$, CM $=x$. We express the area of the triangle in two ways (using Heron's formula and as the semiperimeter multiplied by the radius of the inscribed circle) and obtain the equation:

$$
2(x+20)=\sqrt{(x+20) \cdot x \cdot 6 \cdot 14} \Leftrightarrow \sqrt{x+20}=\sqrt{21 x} \Leftrightarrow x=1 .
$$

Thus, the other two sides of the triangle are 7 and 15.