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Question
In the adjoining figure, AD = CD = BD. ∠ABC is equal to:
Options
80°
90°
95°
100°
MCQ
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Solution
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°.
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