Question

In the following figure, O is the centre of the circle, ∠AOB = 60° and ∠BDC = 100°. Find ∠OBC.

Answer 1

Here, `∠ACB = 1/2 ∠AOB`

= `1/2 xx 60^circ`

= 30°

(Angle at the centre is double the angle at the circumference subtended by the same chord)

By angle sum property of ΔBDC,

∴ ∠DBC = 180° – 100° – 30° = 50°

Hence, ∠OBC = 50°