in a circle

Consider a quarter of a circle (black lines) and the two half circles in it (white).

Can you show that the orange area is equal to the green area?

via DerSpiegel


CapitalistImperialistPig said...

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

wolfgang said...

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.

CapitalistImperialistPig said...

Yes, I meant G, not W.