# Archimedes found found an interesting property of arbelos, that is the area of the circle whose diameter is AH and has common tangent line to the two smaller semicircles at point A is equal to the shaded area. Prove it?

##### 1 Answer

see explanation.

#### Explanation:

Let the three respective semicircles be

Let the areas of

Let the shaded area be

Now let the circle centered at

Let

Another way to find

Now let the area of

Hence,