If the two sides of a pair of opposite sides of a cyclic quadrilateral are equal, prove that its diagonals are equal.

Explanation

Let `ABCD` be a cyclic quadrilateral and `AD=BC`
`AC \and\ BD` are diagonals of cyclic quadrilateral.
In `/_\ AOD \and\ /_\ BOC`
`/_OAD=/_OBC`( Same segment subtends equal angle to the circle)
`AD=BC`(given)
`/_ODA=/_OCB`( Same segment subtends equal angle to the circle)
`/_\ OAD~=/_\ BOC` (Congruence rule)
Adding `/_\DOC` on both sides
`/_\AOD+/_\DOC~=/_\BOC+/_\DOC`
`/_\~=/_\BCD`
`=>AC=BD` (by CPCT)
Hence, we have proved that, a pair of opposite sides of a cyclic quadrilateral are equal prove that its diagonals are also equal