Question

In the given figure, ZADC = 130° and chord BC = chord BE. Find ZCBE.[NCERT C D 130% А 0 В E​

Answer 1

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>>In the given figure, ADC = 130^∘ and ch

Question

In the given figure,∠ADC=130∘ and chord BC = chord BE. Find ∠CBE (in degrees) 

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Solution

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Correct option is A)

In △BCO and △BEO

⇒  BC=BE                 [ Given ]

⇒  ∠BCO=∠BEO              [ Base angles of equal sides are also equal ]

⇒  BO=BO                  [ Common side ]

∴  △BCO≅△BEO             [ By SAS congruence rule ]

⇒  ∠CBO=∠OBE        [ C.P.C.T. ]

Quadrilateral ABCD is a cyclic quadrilateral since, its points lies on a circle.

⇒  ∠ADC+∠CBA=180o            [ Sum of opposite angles of a cyclic quadrilateral is supplementary ]

⇒  130o+∠CBA=180o

⇒  ∠CBA=50o i.e. ∠CBO=50o

∴  ∠OBE=50o

⇒  ∠CBE=50o+50o=100o.

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