Question

If the given figure,o is the centre of the circle.if BD = DC and

Answer 1

In ∆BDC, we have BD = DC (Given)⇒∠BCD = ∠DBC (Angles opposite to equal sides in a ∆ are equal)⇒∠DBC = 30°In ∆BDC,∠BCD + ∠DBC + ∠BDC = 180° [Angle sum property]⇒30° + 30° + ∠BDC = 180° ⇒ ∠BDC = 120°Since, ABDC is a cyclic quadrilateral, so∠BDC + ∠BAC = 180° (Opposite angles of cyclic quad. are supplementary)⇒120° + ∠BAC = 180°⇒∠BAC = 60°We know that angle subtended by an arc at the centre is double the angle subtended by the same arc at any point on the circle.So, ∠BOC = 2∠BAC = 2×60 = 120°