It's as hard as 1-2-3

Geometry Level 5

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

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