# Talk:Arbelos

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Mathematics rating:
 Start Class
 Mid Importance
Field: Geometry

## area property -- why multiply out?

The proof given seems overly complicated.

The area of the circle of diameter h is pi h^2 / 4.

The area of the arbelos is pi/8 - pi r^2/8 - pi (1-r)^2/8

The pythagorean theorem on BHC implies that x^2 + y^2 = 1. But x^2 = r^2 + h^2, and y^2 = h^2 + (1-r)^2.

Thus r^2 + 2h^2 + (1-r)^2 = 1, which implies that h^2 = 1/2 (1 - r^2 - (1-r)^2), and thus pi h^2/4 = pi/8(1 - r^2 - (1-r)^2). QED.

(I'd be tempted to replace "r" and "1-r" with "a" and "b"; r isn't a radius, and the fact that the diameter of the second circle is related to r is only needed in setting up the triangle BHC.) —Preceding unsigned comment added by 149.69.108.48 (talk) 17:10, 8 February 2011 (UTC)