MathDB

nice concyclic

Source: I.F.Sharygin contest 2009 - Correspondence round - Problem 20

May 31, 2009

geometrycircumcirclegeometric transformationreflectiontrigonometrygeometry proposed

Problem Statement

Suppose

H

and

O

are the orthocenter and the circumcenter of acute triangle

ABC

;

AA_1

BB_1

and

CC_1

are the altitudes of the triangle. Point

C_2

is the reflection of

C

A_1B_1

. Prove that

H

O

C_1

and

C_2

are concyclic.