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 \(a+b+c+d\).
by
Daniel Liu