TITLE: What is the area of the circle?
QUESTION [16 upvotes]: In the following diagram, $AB = 4$ and $AC = 3$. What is the area of the circle?
I can't find any way to solve this.

REPLY [3 votes]: Hint:
Let $M$ be the fourth vertex of the rectangle (on the circle), and denote $x$ its polar angle, w.r.t. the polar axis through the centre of the circle. You can express $\sin x$ and $\cos x$ as functions of the radius $R$ of the circle. Then write down Pythagoras' identity $\;\sin^2x+\cos^2x=1\;$ to obtain a quadratic equation for $R$. Don't forget the solution, if any, is subject to the condition $R\ge 4$.