MathDB
Acute triangle, circumcircle, isoceles triangle, altitudes.

Source: Tuymaada 2002, day 2, problem 3. - Author : D. Shiryaev.

May 3, 2007
geometrycircumcircletrigonometrypower of a pointradical axisgeometry proposed

Problem Statement

The points DD and EE on the circumcircle of an acute triangle ABCABC are such that AD=AE=BCAD=AE = BC. Let HH be the common point of the altitudes of triangle ABCABC. It is known that AH2=BH2+CH2AH^{2}=BH^{2}+CH^{2}. Prove that HH lies on the segment DEDE.
Proposed by D. Shiryaev
Back to ProblemsView on AoPS