Four points A, B, C and D lie on a circle, respectively, knowing that AB = CD, prove that ABCD is an isosceles trapezoid.

Question

I try to prove ABCD is a trapezoid buy prove AD//BC but have no idea. Let I be the intersection of AB and CD. I try using thales theorem but still can't.

Answer 1

$\angle CBD = \angle BCA$($\angle$ 's are subtended $=$ segments)

$\angle ABD = \angle DCA$($\angle$ 's are subtended same segments)

Hence $\angle B = \angle C$

$\angle A = 180^o - \angle C$ (opp. $\angle$ 's are supp.)

$AD \parallel BC,(\angle A + \angle B=180^o$, co-interior $\angle$ 's)