Geometric problem Message #1 Posted by Hal Bitton in Boise on 10 Feb 2008, 10:01 p.m.
Hi folks,
Came upon an interesting problem the other day which has been giving me fits ever since. It goes like this:
Consider a circle inscribed in a right triangle such that it just touches all three sides. Describe the ratio of the area of the circle to the area of the triangle solely in terms of r (radius of the circle), and h (hypotenuse of the triangle). I would think there exists a fixed relationship between these two figures, but thus far it eludes me. I'm trying to relate the radius to any one of the sides of the triangle, which is certainly doable given carte blanche to use all the parameters, divide the triangle, etc, but keeping it constrained to just r and h is proving difficult.
Does anybody have any words of wisdom as to how I should attack this thing?
Thanks and best regards, Hal
