And Cn Are Perpendiculars Drawn On Sides And Ab Of Оґabc Prove That Points And Are Concyclic

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


Given In ΔABC, BM ⊥ AC and CN ⊥ AB.
To prove Points B, C, M and N are con-cyclic.
Construction Draw a circle passing through the points B, C, M and N. 

Proof Suppose, we consider SC as a diameter of the circle. Also, we know that SC subtends a 90° to the circle.
So, the points M and N should be on a circle.
Hence, BCMN form a con-cyclic quadrilateral. Hence proved.