Given a right triangle, draw the three following semicircles:

1. The semicircle with diameter formed by one of the legs and extending away from the triangle.
   
2. The semicircle with diameter formed by the other leg and extending away from the triangle.
   
3. The semicircle with diameter formed by the hypotenuse and extending towards the triangle.

Prove that the area of the two crescents (shown in RED and BLUE) formed by the three semicircles equals the area of the triangle.

I like this problem because the truth is not intuitively obvious from the picture, and yet the math is very easy.

Posted by Larry on 2004-08-11 08:23:27