MathDB
constructed triangle is right-angled

Source: China Team Selection Test 2003, Day 1, Problem 1

October 13, 2005
geometrycircumcircletrigonometryangle bisectorgeometry solved

Problem Statement

ABCABC is an acute-angled triangle. Let DD be the point on BCBC such that ADAD is the bisector of ∠A\angle A. Let E,FE, F be the feet of perpendiculars from DD to AC,ABAC,AB respectively. Suppose the lines BEBE and CFCF meet at HH. The circumcircle of triangle AFHAFH meets BEBE at GG (apart from HH). Prove that the triangle constructed from BGBG, GEGE and BFBF is right-angled.
Back to ProblemsView on AoPS