# Inspired by My Best Friend - 2

Geometry Level 5

Let '$$P$$' and '$$Q$$' be two conjugate points with respect to the circle of radius $$20$$ units. Let the lengths of the tangents from $$P$$ and $$Q$$ onto circle be $$20$$, $$24$$ respectively.

If the length of the segment $$PQ$$ can be expressed in the form of $$a\sqrt{b}$$; where $$a$$, $$b$$ are positive integers and $$b$$ is square free. Find $$a+b$$.

Details and Assumptions:

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