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 .
∠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