Question

In the adjoining figure, AD = CD = BD. ∠ABC is equal to:

विकल्प

• 80°

• 90°

• 95°

• 100°

Answer 1

90°

Explanation:

AD = CD

⇒ D is the midpoint of AC. 

Also, BD = AD = CD.

So, D is equidistant from A, B and C, i.e. D is the circumcenter.

A circumcenter lying on side AC means AC is a diameter of the circumcircle.

So, the angle subtended by AC at B is a right angle (Thales’ theorem). 

Therefore, ∠ABC = 90°.