Question

Prove that in a cyclic trapezium the non parallel sides are equal

Answer 1

Question :- Prove that in a cyclic trapezium the non parallel sides are equal.

Answer :- Let ABCD be the cyclic trapezium in which AB||CD.
We have to prove that AD = BC
Since AB||CD and BD is the transversal, we have
∠ABD = ∠BDC [Alternate angles]
Also chord AD subtends ∠ABD and chord BC subtends ∠BDC on the circle at B and D respectively.
Also ∠ABD =∠BDC (proved above)
Therefore, AD = BC