Consider a right triangle with an inscribed circle. Let x and y be the lengths of the two line segments formed on the hypotenuse by the point of tangency with the circle. What interesting fact can you prove about x*y?

(In reply to No Subject by TomM)

Area = inradius x semiperimeter is a neat formula that works for other figures besides triangles.  For example, it works beautifully for a regular hexagon of side 1 to give 3*sqrt(3)/2 ~= 2.6 as the area.  The American Mathematical Monthly of Dec. 2004 has a nice article on the subject: "Figures Circumscribing Circles" by Tom M. Apostol and Mamikon A Mnatsakanian.

Posted by Richard on 2005-03-01 16:56:57