MathDB

Reflection of the orthocenter

Source: Indian IMOTC 2013, Team Selection Test 1, Problem 2

May 15, 2013

geometrygeometric transformationreflectioncircumcircletrigonometryparallelogramhomothety

Problem Statement

In a triangle

ABC

, with

\widehat{A} > 90^\circ

, let

O

and

H

denote its circumcenter and orthocenter, respectively. Let

K

be the reflection of

H

with respect to

A

. Prove that

K, O

and

C

are collinear if and only if

\widehat{A} - \widehat{B} = 90^\circ