Question

If BM and CN are the perpendiculars drawn on the sides AC and AB of the triangle ABC , so the points B, C, M and N are concyclic?

Answer 1

As $BM$ and $CN$ are the perpendicular drawn on the sides $AC$ and $AB$ of the triangle $ABC$

Refer image,

$\therefore \angle BMC=\angle BNC={90}^0$

Since, if a line segment (here $BC$) joining two points (here $B$ and $C$) subtends equal angles ($here\angle BMCand\angle BNC$) at $M$ and $N$ on the same of the line (here $BC$) containing the segment, the four points (here $B,C,M$ and $N$) are concylic.