Let $AD$ be an altitude in a right $\triangle ABC$ with $\angle A =90°$ and $D$ on $BC$.
Suppose that the radii of the incircles of the $\triangle ABD $and $\triangle ACD$ are 33 and 56 respectively.
Let $r$ bet the radius of the$ \triangle ABC $ , find the value of $3(r+7)$.
I found the radius to be 65 and the answer to be 216 by similarity but I want to know if my answer is correct or not and also any another method if there is any.