two lines OAB and OCD drawn from an exterior point O to a circle intersect at A and B , and C and D respectively.Prove that angle ODA is equal to angle OBC
Answers
Given : Lines OAB & OCD are drawn from an exterior point O to a circle
intersect at A and B , and C and D respectively
To Find : Prove that angle ODA is equal to angle OBC
∠ODA = ∠OBC
Solution:
∠ABC = ∠ADC
Angle by same arc AC at remaining arc segment
∠ABC = ∠OBC as A lies on OB
∠ADC = ∠CDA
∠CDA = ∠ODA as C lies on OD
=> ∠ADC = ∠ODA
∠ABC = ∠ADC
∠ABC = ∠OBC
∠ADC = ∠ODA
=> ∠OBC = ∠ODA
∠ODA = ∠OBC
QED
Hence Proved
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Answer:
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