<Tri-2026-2818>, hint

 

 <Tri-2026-2818>,general. bisector

<Taiwan Math TST3 2014>

<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.