<Tri-2026-2376>, hint

 Since AE=AF, BF=BD, CD=AE

(AF/FB)x(BD/DC)x(CE/EA)=1,

By Menelaus Theorem ;(AF/FB)x(BT/TC)x(CE/EA)=1

Hence  BD/DC=BT/TC  (T,D;B,C)=-1

<Tri-2026-2376>, general.cyclic

<Spain MO 2022>

 

<Solid-2026-271>, hint

 

<Solid-2026-271>, tetrahedron, angle

<Spain MO 2021>

 

<Tri-2026-2375>, hint