Question

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

Answer 1

Given : In cyclic quadrilateral ABCD, AB = CD. AC and BD are the diagonals.

To prove : AC = BD

Proof : $\because AB=CD$

$\therefore$ arc AB = arc CD

Adding arc BC to both sides, arc AB + arc BC = arc BC + arc CD

$\Rightarrow arcAC=arcBD$

$\therefore AC=BD$

Hence, diagonals of the cyclic quadrilateral are equal.