In figure, ∠ADC = 130° and chord BC = chord BE. Find ∠CBE. - Mathematics

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Sum

In figure, ∠ADC = 130° and chord BC = chord BE. Find ∠CBE.

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Solution

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

ABCD is a cyclic quadrilateral.

As, the sum of opposite angles of a cyclic quadrilateral is 180°.

∠ADC + ∠ABC = 180°

 130° + ∠ABC = 180°

∠ABC = 180° – 130° = 50°

⇒ ∠OBC = 50°

In ΔBCO and ΔBEO

BC = BE  .....[Given equal chord]

∠BCO = ∠BEO [Angles opposite to equal sides]

OB = OB   .....[Common side]

∴ By SAS congruence

ΔBCO ≅ ΔBEO

∴ ∠OBC = ∠OBE

∴ ∠OBE = 50°   .....[∠OBC = 50°]

Now, ∠CBE = ∠CBO + ∠OBE

= 50° + 50° = 100°

Hence, the angle ∠CBE is 100°. 

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Chapter 10: Circles - Exercise 10.3 [Page 104]

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NCERT Exemplar Mathematics Class 9
Chapter 10 Circles
Exercise 10.3 | Q 15 | Page 104

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