# SAT Deja vu

Geometry Level 5

Let $A,B,C,D$ be points on a line in that order and $AC=11, BC=5, BD=60$. The circles with diameters $AC,BD$ intersect at $E,F$. Let $P$ be a point on the circle with diameter $AD$ such that $P,F$ are on the same side of $AD$ and $AP=DP$. Find $PE$

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