Prove that, given two chords on circle O labeled AB and CD, and given that arc AC and arc BD are equal, that AB=CD

Question

Prove that, given two chords on circle $O$ labeled $AB$ and $CD$, and given that arcs $AC$ and arc $BD$ are equal, then $AB\parallel CD$.

I understand that they are parallel, but I need help forming a proof to prove it. Thanks!

Answer 1

Here are hints for two different ways to prove it.

Hint 1: Draw $BC$, and think about the angles $ABC$ and $BCD$.

Hint 2: Draw a diameter through the midpoint of $CD$. Think about what happens when you reflect the picture across this diameter.