MathDB

Suppose

H

and

O

are orthocenter and circumcenter of triangle

ABC

\omega

is circumcircle of

ABC

AO

intersects with

\omega

A_1

A_1H

intersects with

\omega

A'

and

A''

is the intersection point of

\omega

and

AH

. We define points

B',\ B'',\ C'

and

C''

similiarly. Prove that

A'A'',B'B''

and

C'C''

are concurrent in a point on the Euler line of triangle

ABC

Problem Statement