Geometric problem - Printable Version +- HP Forums ( https://archived.hpcalc.org/museumforum)+-- Forum: HP Museum Forums ( https://archived.hpcalc.org/museumforum/forum-1.html)+--- Forum: Old HP Forum Archives ( https://archived.hpcalc.org/museumforum/forum-2.html)+--- Thread: Geometric problem ( /thread-132642.html) |

Geometric problem - Hal Bitton in Boise - 02-10-2008
Hi folks,
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. Re: Geometric problem - Monte Dalrymple - 02-10-2008
Well, it's been more years than I care to admit, but...
for right triangle with sides a, b and h; area of triangle = ab/2 = r^2 + r(a-r) + r(b-r) = r(a + b - r) but we also have h = (a - r) + (b - r) so (a + b - r) = (h + r) substituting gives area of triangle = r(h + r)
Re: Geometric problem - Hal Bitton in Boise - 02-11-2008
Many thanks Monte... |