<Tri-2026-2334>, hint

 

<Tri-2026-2337>, general, others

 

<Tri-2026-2336>, general , others

<South Africa MO 2019>

 

<Tri-2026-2335>, hint

since HPDEF are concyclic

EF/sin EHF=EF/sinA=2PH---<1>, BC/sinA=2R---<2>

<1>/<2>=EF/BC= 2PH/2R. Similarly DE/AB=FD/AC=2PH/2R

Two triangles are similar Hence  ratio of their areas is (2PH/2R) x (2PH/2R)

<Tri-2026-2335>, general, similar

<South Africa MO 2018>