MathDB

Orthocenter and Incenter

Source: Bulgarian IMO TST 2005, Day 2, Problem 2

July 7, 2013

geometryincentercircumcircletrigonometrytrapezoidgeometric transformationreflection

Problem Statement

Let

ABC

AC \not= BC

, be an acute triangle with orthocenter

H

and incenter

I

. The lines

CH

and

CI

meet the circumcircle of

\bigtriangleup ABC

at points

D

and

L

, respectively. Prove that

\angle CIH = 90^{\circ}

if and only if

\angle IDL = 90^{\circ}