# Geometry with a Square

Geometry Level 3

Let $$M$$ be an arbitrary point inside a unit square $$ABCD$$. Consider points $$P, Q, R$$ defined as points of intersection of medians of $$\triangle ABM, \triangle BCM, \triangle CDM$$. The length of the segment between $$P$$ and midpoint of $$QR$$ can be expressed as $$\frac{a \sqrt{b}}{c}$$, find $$a + b + c$$.

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