# Qi Huan's square

Geometry Level 3

$$ABCD$$ is a square with side length $$10$$ and $$P$$ is a point in the interior of $$ABCD$$ such that $$PA=6$$ and $$PB=8$$. If the length of $$PC$$ is written as $$a\sqrt{b}$$, where $$a$$ and $$b$$ are positive integers, and $$b$$ is not a multiple of the square of any prime, what is the value of $$a+b$$?

This problem is posed by Qi Huan T.

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