MathDB

ABC

is a triangle with orthocenter

H

. The median from

A

meets the circumcircle again at

A_1

, and

A_2

is the reflection of

A_1

in the midpoint of

BC

. The points

B_2

and

C_2

are defined similarly. Show that

H

A_2

B_2

and

C_2

lie on a circle. https://cdn.artofproblemsolving.com/attachments/f/1/192d14a0a7a9aa9ac7b38763e6ea6a4a95be55.png

Problem Statement