From a triangle, three triangles were cut off, and each of the three cuts touched the inscribed circle of the triangle. It is known that the perimeters of the cut-off triangles are $P_{1}, P_{2}, P_{3}$. Find the perimeter of the original triangle.
We will paint with one color the segments of tangents drawn from one point to a circle - in total, six pairs of equal tangent segments are obtained. In the described hexagon, formed after cutting off the triangles, the three sides along which the cuts are made are composed of six segments of different colors. The remaining three sides are also composed of six segments of different colors. Therefore, the sum of the lengths of the three cuts is equal to the sum of the three segments of the perimeter of the original triangle, not belonging to the cut-off triangles. From this, it is easy to see that the perimeter of the original triangle is equal to the sum of the perimeters of the cut-off triangles.

## Otvet

$P_{1}+P_{2}+P_{3}$