# A geometry problem by ritwik jain

Geometry Level 4

Let $$AD$$ be an altitude in a right triangle $$ABC$$ with $$\angle A = 90^\circ$$ and $$D$$ on $$BC$$. Suppose that the radii of the incircles of the $$\triangle ABD$$ and $$\triangle ACD$$ are 33 and 56 respectively. Let $$r$$ be the radius of the incircle of the $$\triangle ABC$$. Find the value of $$r$$.

×