<Tri-2026-2307>, hint

 

<Tri-2026-2307>,general, cyclic

<Singapore MO 2008>

 

<Tri-2026-2306>, hint

 

<Tri-2026-2306>, isosceles , tangent

<Singapore MO 2007>

<Tri-2026-2305>, hint

DE//BC, DE=1/2 BC. Since triangle ADN, 30-60-90 AN=2AD=AC

Similarly AM=2AE=AB. Hence triangles ABC and AMN are congruent MN=BC

Triangle EMN is right triangle and L is the midpoint of MN Hence EL=LN=LM=1/2MN

=1/2BC. ED=EL =1/2BC. finally <EDL=<ELD