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,


ΔBOC ΔBOE


By CPCT,


⇒∠OBC = OBE = 50°


⇒∠CBE = CBO + EBO


= 50° + 50°


CBE = 100°


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