MathDB

Let

ABC

be an acute triangle with circumcenter

O

and orthocenter

H

. The circle with center

X_A

passes through the points

A

and

H

and is tangent to the circumcircle of the triangle

ABC

. Similarly, define the points

X_B

and

X_C

. Let

O_A

O_B

and

O_C

be the reflections of

O

with respect to sides

BC

CA

and

AB

, respectively. Prove that the lines

O_AX_A

O_BX_B

and

O_CX_C

are concurrent.

Problem Statement