Let A B C be a triangle with B A C=90^ and D be the point on the...

Let $A B C$ be a triangle with $\angle B A C=90^{\circ}$ and $D$ be the point on the side $B C$ such that $A D \perp B C$. Let $r, r_1$, and $r_2$ be the inradii of triangles $A B C, A B D$ and $A C D$, respectively. If $r, r_1$, and $r_2$ are positive integers and one of them is 5 , find the largest possible value of $r+r_1+r_2$.