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Question
In the given figure, A is the centre of the circle, ABCD is a parallelogram and CDE is a straight line. Prove that : ∠BCD = 2∠ABE.
Solution
∠BAD = 2∠BED
(Angle at the centre is double the angle at the circumference subtended by the same chord)
And ∠BED = ∠ABE (Alternate angles)
∴ ∠BAD = 2∠ABE ...(i)
ABCD is a parallelogram
∴ ∠BAD = ∠BCD ...(ii)
(Opposite angles in a parallelogram are equal)
From (i) and (ii),
∠BCD = 2∠ABE
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