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  • 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.

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.

Answers (1)

Given: In DABC, MB\perp AC and CN \perp AB.

To Prove: Points B, C, M and N are Concyclic (lie on the same circle)

Proof:

Assume, BC is the diameter of a circle.

So BC will subtend an angle of 90° at any point on the circle.

Now, MB \perp AC and CN \perp AB. So these angles lie on the circle and the points N and M lie on this circle.

Hence, BCMN is concyclic.

Hence Proved.   

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