If in a cyclic quadrilateral `ABCD, AB=DC`, then prove that AC=BD

Explanation

In the cyclic quadrialteral `ABCD,=AB=DC`
`:.` the angles in cricle produced by the chords Aband CD are equal.
`:. angle ACB= angle ADB ....... (1) and `
`angle CBD= angleCAD .....(2)`
Moreover `angle ACB= angleCBD[ :. AB =DC]`
in `Delta EBC, angle ECB angleEBC, :. BE= CE`

Again `angle ADB= angle CAD [ :. AB= DC]`
`:. "in" Delta EAD, angle EAD= angle EDA :. DE=AE`
Now, `AE+ CE=DE [ :. AE= DE and CE= BE] or, AC= BD`