Answer to Question #180489 in Geometry for Harshit bareja

Question

The sides a, b, c of a right triangle, where c is the hypotenuse, are circumscribing a circle.

Prove that the radius r of the circle is given by r = (𝑎+𝑏−𝑐)

2

.

Answer 1

Let circle touch CB at M and CA at N, AB at P