<Tri-2026-2817>, hint

 

<Tri-2026-2817>, general. center

<Taiwan MO 2002>

 

<Tri-2026-2816 >, hint

Since M is the center of circle ABPQ ,by Brocard theorem M is the orthocenter 0f triangle CHT and CMㅗTH.

<Tri-2026-2816> , general, orthocenter

<Taiwan MO 2000>

<Solid-2026-275>, hint