AB and AC are equal chords of a circle. AD and BE are parallel chords through A and B respectively. Prove that AE is parallel to CD.
Note that if a cyclic quadrilateral is a trapzeium , then it is an isosceles trapzeium . If a pair of the opposite sides are equal in length , then it is also an isosceles trapzeium .
To prove the first line , Let $\displaystyle ABCD $ is a cyclic quadrilateral , assume it is a trapzeium , say $\displaystyle AB \parallel CD $ , then we have $\displaystyle \angle ABD = \angle BDC $ so $\displaystyle \text{arc} AD = \text{arc} BC \implies AD = BC $ thus it is an isos. trapzeium .
I give the proof of the second line to you .
By applying the above property , we find that $\displaystyle DE = AB = AC $ so $\displaystyle AE \parallel CD$