Thread: Circle Geometry: Difficult Proving Parrallel Lines

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 is a cyclic quadrilateral , assume it is a trapzeium , say , then we have so thus it is an isos. trapzeium .

I give the proof of the second line to you .


By applying the above property , we find that so

Sorry, I am not so sure ABCD is concyclic. As ABCE is the actual quad inside circle.

EDIT: nvm, i have found solution anywaz.