Question

If quadrilateral ABCD is cyclic, then find the angle subtended at the centre by vertex B and D i.e. $\angle BOD.$

• A. ${50}^{\circ }$
• B. ${45}^{\circ }$
• C. ${30}^{\circ }$
• D. ${60}^{\circ }$

Answer 1

The correct option is D ${60}^{\circ }$

Since, ABCD is cyclic.

$\therefore \angle C+\angle A={180}^{\circ }$

(Sum of opposite angles in a cyclic quadrilateral is 180)

$150+\angle A={180}^{\circ }$

$\angle A={30}^{\circ }$

Now,

$\angle BOD=2\angle BAD$

(An angle subtended by an arc at the centre is twice the angle subtended by the same arc at the circumference)

$\text{So},$
$\angle BOD=2\times {30}^{\circ }$

$={60}^{\circ }$