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If BM and CN are the perpendiculars draw...

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

Text Solution

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Given In `DeltaABC, BM bot AC and CN bot 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 BC as a diameter of the circle. Also, we know that BC subtends a `90^(@)` to the circle.
So, the points M and N should be on a circle.
Hence, BCMN form a con-cyclic quadrilateral.
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