Question 1 0If BM and CN are the perpendiculars drawn on the sides AC and AB of the - ABC- prove that the points B - C - M and N are concyclic-

Given in Δ ABC, BM ⊥ AC and CN ⊥ AB. To prove that points B, C, M and N are concyclic. Construction : nbsp;Draw a circle passing through the points B, C, M an ...

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Standard IX

Mathematics

Perpendicular from the Center to a Chord Bisects the Chord

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Question 10
If BM and CN are the perpendiculars drawn on the sides AC and AB of the $Δ A B C$ , prove that the points B, C, M and N are concyclic.

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Solution

Given in $Δ A B C, B M ⊥ A C a n d C N ⊥ A B$ .
To prove that points B, C, M and N are concyclic.
Construction : Draw a circle passing through the points B, C, M and N.Proof
Suppose we consider BC as the diameter of the circle. Also, we know that BC subtends a $90^{\circ}$ to the circle.
So, the points M and N should be on a circle.
Hence, BCMN from a concyclic quadrilateral.

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Question 10 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.

Question 10
If BM and CN are the perpendiculars drawn on the sides AC and AB of the $Δ A B C$ , prove that the points B, C, M and N are concyclic.