Hippocrates of Chios found this 2,400 years ago, long before anyone could work out a curved area. C is on the circle, so the angle at C is a right angle. Draw a half circle on each short side: the two moons left outside the big circle have exactly the area of the triangle.
The source code is at github.com/KirillOsenkov/LiveGeometry. It is written in .NET and Avalonia.