Question

If a pair of opposite sides are equal of a cyclic quadrilateral , Prove the diagonals are also equal

Answer 1

Proof Clearly
BD = BD (common)
CBD = ADB (alternate angle)
BDC = ABD (alternate angle)

So Δ ADB ≈ Δ CDB
Similarly Δ ADC ≈ Δ CBA
So Diagonals are equal.. :)