Find the area of the red region.

Two circles are intersecting to each other at points P and R. Points O and Q are the centres of the larger and smaller circle. The radius of the larger and smaller circle is √6 and √3, respectively. Find the area of the red region.

[philippeganty]

Why do you use trigonometry when we can easily prove by Pythagoras that the triangle PQO is right-angled and isosceles of type 1/1/√2?

[larrydickenson]

You already know that angle theta is 45 degrees since the triangle is isosceles.