MathDB
Geometry from Colombia

Source: Colombia 2020

February 16, 2022
Columbiageometry

Problem Statement

Given an acute-angled triangle ABCABC with DD is the foot of the altitude from A.A. The perpendicular lines to BCBC through BB and CC intersect the altitudes from CC and BB at points MM and NN, respectively. Show that ADAD == BCBC if and only if A,M,NA,M,N and DD lie on the same circle.
Back to ProblemsView on AoPS