MathNet 2021 — Part 03 Question 52

Let $D$ be the foot of the altitude drawn to the hypotenuse $AB$ of a right triangle $ABC$. The inradii of the triangles $ABC$, $CAD$ and $CBD$ are $r$, $r_1$ and $r_2$, respectively. Prove that $CD = r + r_1 + r_2$.