MathDB

Let

ABC

be an acute triangle with orthocenter

H

and let

X

be an arbitrary point in its plane. The circle with diameter

HX

intersects the lines

AH

and

AX

A_{1}

and

A_{2}

, respectively. Similarly, define

B_{1}

B_{2}

C_{1}

C_{2}

. Prove that the lines

A_{1}A_{2}

B_{1}B_{2}

C_{1}C_{2}

are concurrent. Remark. The triangle obviously doesn't need to be acute.

Problem Statement