# It's as hard as 1-2-3

Geometry Level 5

A circle with center $$O$$ has two points $$A,B$$ on its circumference and one point $$P$$ inside the circle such that $$AP=1$$, $$BP=2$$, $$OP=3$$, and $$\angle APB=90^{\circ}$$. If the area of the circle can be expressed as $\left(\dfrac{a+b\sqrt{c}}{d}\right)\pi$ for positive integers $$a,b,c,d$$ such that $$c$$ is square-free and $$a,b$$ are coprime with $$d$$, then find the value of $$a+b+c+d$$.

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