Question 10If 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 ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard IX

Mathematics

Circles

Question 10If...

Question

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.

Open in App

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.

Suggest Corrections

Similar questions

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

Q. 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?

In a $Δ A B C$ , M and N are points on the sides AB and AC respectively such that BM = CN. If $∠ B = ∠ C$ then show that MN || BC.

D and E are points on equal sides AB and AC of an isosceles triangle ABC such that AD = AE.

Prove that the points B, C, E and D are concyclic.

Q. In △ABC, M and N are points on AB and AC respectively such that BM = CN. If ∠B = ∠C then show that MN∥BC.

Join BYJU'S Learning Program

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.