# Trig-gono-metry-1

Geometry Level 3

In a rectangle $$ABCD$$ with sides $$AB=6$$ and $$BC=3$$, point $$P$$ is chosen on $$AB$$ such that $$\angle APD = 2\angle CPB$$. Then $$AP= a-b\sqrt c$$, where $$a$$, $$b$$ and $$c$$ are positive integers with $$c$$ being square-free. Find the value of $$a+b+c$$.

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