<Tri-2026-2322>, hint

 

<Tri-2026-2322>,isosceles, tangent

<South Africa MO 2004>

 

 <Polygon-2026-279>, hint

since [BCD]=[ECD].BE//CD

Similarly BC//AD, DE//AC. BCDN and EDCM are parallelogram

and CD=BN=EM, BM=BN-MN=NE=EM-MN

<Polygon-2026-279>, pentagon, parallel

<South Africa MO 2003>

 

<Tri-2026-2321>, hint