MathDB

Orthocenter, circumcenter and perperdicular segments

Source: All-Russian MO Round 4, 2005

April 2, 2005

geometrycircumcirclepower of a pointradical axisgeometry proposed

Problem Statement

11.4 Let

AA_1

and

BB_1

are altitudes of an acute non-isosceles triangle

ABC

A'

is a midpoint of

BC

and

B'

is a midpoint of

AC

. A segement

A_1B_1

intersects

A'B'

at point

C'

. Prove that

CC'\perp HO

, where

H

is a orthocenter and

O

is a circumcenter of

ABC

. (L. Emel'yanov)