The sum of triangles' area
Source: Indonesia Mathematics Olympiad 2008 Day 2 Problem 3
August 13, 2008
geometryinradiusratiogeometry proposed
Problem Statement
Given triangle with sidelengths . Tangents to incircle of that parallel with triangle's sides form three small triangle (each small triangle has 1 vertex of ). Prove that the sum of area of incircles of these three small triangles and the area of incircle of triangle is equal to
\frac{\pi (a^{2}\plus{}b^{2}\plus{}c^{2})(b\plus{}c\minus{}a)(c\plus{}a\minus{}b)(a\plus{}b\minus{}c)}{(a\plus{}b\plus{}c)^{3}}
(hmm,, looks familiar, isn't it? :wink: )