What is the length of the diameter of a circle inscribed in a right triangle with the length of hypotenuse c and the sum of the legs' lengths equal to m?

Question

Please solve for d = _______

(using the variables in the question)

Answer 1

I doubt it will be possible to solve this problem UNLESS you draw a figure.

Let the hypotenuse be divided into 2 parts by the line joining the center to the tangent; call them a and b.

The legs will then be r+a and r+b because there are 2 sets of congruent triangles and a square in the right angle corner of the right triangle.

Therefore we have (a+r) + (b+r) = m and c + 2 r = m => 2r = d = m-c