If the radius of the quarter circle is r, it has area pi*r^2/4. The half circles each have area pi*r^2/8, so their combined area should equal the area of the quarter circle. If the overlap is O for Orange, we have 2(pi*r^2/8)-O + W(hite) = pi*r^2/4. Hence O = W

I don't understand your O=W result, but I think you got the main point right: The area of the quarter circle equals the area of the two (white) half circles; but we also have: area of quarter circle = green area + area of two white half circles - orange area. It follows that O = G.

## 3 comments:

If the radius of the quarter circle is r, it has area pi*r^2/4. The half circles each have area pi*r^2/8, so their combined area should equal the area of the quarter circle. If the overlap is O for Orange, we have 2(pi*r^2/8)-O + W(hite) = pi*r^2/4. Hence O = W

I don't understand your O=W result, but I think you got the main point right:

The area of the quarter circle equals the area of the two (white) half circles;

but we also have: area of quarter circle = green area + area of two white half circles - orange area.

It follows that O = G.

Yes, I meant G, not W.

Doh!

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