A circle with radius r is inscribed into a right triangle. Find the perimeter of the triangle if: The point of tangency divides the hypotenuse into 5 cm and 12 cm segments.

Answer 1

It will be difficult, if not impossible, to solve this problem without drawing a figure.

When you do you should pretty quickly see that one of the legs of right triangle is 12+r and the other is 5+r.

Then you have (5+r)² + (12+r)² = (5+12)² = 289.

Expand and collect terms and you will have a quadratic equation is r.

Solve the quadratic and you will be able to compute the perimeter.