MathDB

Turkey NMO 2004 P.1, Easy Problem

Source:

December 11, 2010

geometryparallelogramtrapezoidrectangleangle bisectorgeometry proposed

Problem Statement

In a triangle

\triangle ABC

with

\angle B>\angle C

, the altitude, the angle bisector, and the median from

A

intersect

BC

H, L

and

D

, respectively. Show that

\angle HAL=\angle DAL

if and only if

\angle BAC=90^{\circ}