Q 17 In the above figure ABCD is a cyclic quadrilateral and angle BCD = 2 angle BAD - Maths - Understanding shapes

Question

Q 17 In the above figure ABCD is a cyclic quadrilateral and angle
BCD = 2 angle BAD Find the angle made by the diagonal BD at the
centre of the circle

Lovina Kansal · Accepted Answer

Dear student

In cyclic quadrilateral opposite angles are supplementary
So, ∠BCD+∠BAD=180°⇒∠2BAD+∠BAD=180°   ∵∠BCD=2∠BAD   given⇒3∠BAD=180°⇒∠BAD=60°Angle made by arc BD at centre=2∠BAD=2×60°=120°      ∵The angle subtended by an arc at the centre of a circle is double the angle subtended by it at any point on the remaining part of the circle
Regards

Q.17. In the above figure ABCD is a cyclic quadrilateral and angle BCD = 2 angle BAD. Find the angle made by the diagonal BD at the centre of the circle.