# Suli's geometry problem

Geometry Level 5

Let $$ABC$$ be a triangle with $$AB = 17, AC = 25, BC = 28$$. The triangle has circumcircle $$\Gamma$$ and incenter $$I$$. Point $$D$$ is on $$\Gamma$$ such that $$\angle ADI = 90^{\circ}$$, and extend $$AI$$ to meet $$BC$$ at $$E$$. If $$\sin^2 \angle IDE$$ can be represented as $$\frac{m}{n}$$ with $$m$$ and $$n$$ are coprime positive integers, compute $$m+n$$.

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