<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

 

<Solid-2026-275> tetrahedron, area

<Taiwan MO 1997>

 

<Tri-2026-2815>, hint

Consider equilateral triangle ABC and a right triangle 30-60-90.