# Inspired by Euler

Geometry Level 5

Given triangle $$ABC$$ with $$AB=20, AC=34$$, define $$D\in BC$$ such that $$AD\perp BC$$ and $$AD=16$$. $$P$$ is a point on segment $$AD$$ such that if $$K$$ is the foot of projection from $$P$$ to $$AB$$, then $OP^2=R(R-2PK)$where $$O,R$$ are the circumcenter and circumradius respectively.

Find the length of $$AP$$.

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