Question

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

Answer 1

According to the question,

BM and CN are the perpendiculars drawn on the sides AC and AB of the triangle ABC.

So, we have,

∠BMC = ∠BNC = 90^o

We know that,

If a line segment joining two points subtends equal angles on the same side of the line containing the segment, then the four points are concyclic.

Considering the question,

Since BC joins the two points, B and C, subtending equal angles, ∠BMC and ∠BNC, at M and N on the same side BC containing the segment, then B, C, M and N are concyclic.

Hence, we get that, B, C, M and N are concyclic.