Question

Prove that an isoceles trapezium is always cyclic

Answer 1

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)

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