Posted by **dgibson** on Thursday, November 23, 2006 at 12:00am.

Suppose we draw semicircles on the sides of a triangle and compute their areas. If the sum of the areas of two of the semicircles equals the area of the third, is the triangle a right triangle?

Yes.

(pi/2)(a^2 + b^2) = (pi/2) c^2

if and only if

a^2 + b^2 = c^2,

and that requires a right angle triangle.

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