# A complicated circle inside a square

Geometry Level 4

Given a circle is inscribed in a square $$ABCD$$ with sides of length $$12$$. Point $$M$$ is on $$AB$$ such that $$AM=5$$. Let $$P$$ and $$Q$$ be points of intersections of $$MD$$ and the circle, with $$P$$ closer to $$AB$$. If the length of $$MP=\frac{a-b\sqrt{c}}{d}$$ in simplest form, find $$a+b+c+d$$

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