A Line through the Center That Bisects the Chord Is Perpendicular to the Chord.
If BM and CN ...
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?
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As BM and CN are the perpendicular drawn on the sides AC and AB of the triangle ABC
Since, if a line segment (here BC) joining two points (here B and C) subtends equal angles (here∠BMCand∠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.