Hi everyone! This is a problem from the last class of my geometry course, and I am a bit stuck on it. The week focus is "challenging problems", so I know that it is meant to be hard and I just need a hint to get started, because I don't know how to. Thank you in advance!
A circle is centered at O and has an area of 48*pi. Let Q and R be points on the circle, and let P be the circumcenter of triangle QRO. If P is contained in triangle QRO, and triangle PQR is equilateral, then find the area of triangle PQR.
As an equilateral triangle, the area of triangle PQR works out to 48*sqrt(3).