<Tri-2026-2374>, hint

 

<Tri-2026-2374>, general,  area

<Spain MO 2018>

<Tri-2026-2373>, hint

Since DM, DN are angle bisector AD/BD(=CD)=AM/MB=AN/NC 

MN//BC. Hence EF//MN//BC//PR.

Since <MDN=90, MO=NO, OD=OM=ON, FN/FR=FO/FP=ON/PR (  ON=OD)

You can prove PR=AD

<Tri-2026-2373>, general, parallel

<Spain MO 2017>

 

<Tri-2026-2372>, hint