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.

Answer 1

∠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