A circle with a radius of 4 is inscribed in a right triangle, the hypotenuse of which is 26. Find the perimeter of the triangle.

#
Tangents drawn from a single point to a circle are equal to each other.

## Solution

The sum of the segments connecting the vertices of the acute angles to the points of tangency of the inscribed circle with the legs is equal to the hypotenuse. By adding two radii of the circle to this sum, we get the sum of the legs.

![](https://cdn.mathpix.com/cropped/2024_05_06_4fce0705b02fa9e106d4g-06.jpg?height=308&width=580&top_left_y=692&top_left_x=745)

Answer

60.