Answer :

Given ADC = 130° and chord BC = chord BE.

Consider the points A, B, C and D which form a cyclic quadrilateral.

We know that in a cyclic quadrilateral the opposite angles are supplementary.

In cyclic quadrilateral ADCB,

⇒∠ADC + OBC = 180°

130° + OBC = 180°

⇒∠OBC = 180° - 130° = 50°

Consider ΔBOC and ΔBOE,

BC = BE [given]

OC = OE [radii of same circle]

OB = OB [common side]

By SSS congruence rule,



⇒∠OBC = OBE = 50°


= 50° + 50°

CBE = 100°

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