Pre-RMO Question!

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 triangles \(ABD\) and \(ACD\) are \(33\) and \(56\) respectively. Let \(r\) be the radius of the incircle of triangle \(ABC.\) Find the value of \(3(r + 7).\)

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