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 \(r\).

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