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

3 comments:

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.

Doh!