Write True or False and justify your answer in each of the following: If A, B, C, D are four points such that \angle BAC = 30^{\circ} \;\; and \;\;\angle BDC = 60^{\circ}, then D is the centre of the circle through A, B and C.

Answers (1)

True

Solution:

Given, ∠BAC = 30° and ∠BDC = 60°

We know that,

The angle subtended at the centre by an arc is twice the angle subtended by it at any part of the circle.

Considering BC,

At centre, \angle BDC = 60^{\circ}

At any other point on the circle,

\angle BAC = 30^{\circ}=\frac{1}{2} (60^{\circ})

Hence the above rule is justified.

Therefore the given statement is true.

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