Question

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

Answer 1

Answer:

Let ABCD be a cyclic quadrilateral and AB = CD.

⇒ arc AB = arc CD (Corresponding arcs of the equal chords)

Adding arc AD to both the sides of the equation;

arc AB + arc AD = arc CD + arc AD

∴ arc BAD = arc CDA

⇒ Chord BD = Chord CA

⇒ BD = CA