KöMaL 2025 B5495

The legs of a right triangle are $a$ and $b$ , its hypotenuse is $c$ , and its inradius is $r$ . Prove that $2r^2=(c-a)(c-b).$

Official text KöMaL. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.