Question

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

Answer 1

Step-by-step explanation:

Given Let ABCD be a cyclic quadrilateral and AD = BC

Join AC and BD.

To prove AC = BD

Proof In ΔAOD and ΔBOC,

∠OAD = ∠OBC and ∠ODA = ∠OCB

[since, same segments subtends equal angle to the circle]

AB = BC [given]

ΔAOD = ΔBOC [by ASA congruence rule]

Adding is DOC on both sides, we get

ΔAOD+ ΔDOC ≅ ΔBOC + ΔDOC

⇒ ΔADC ≅ ΔBCD

AC = BD [by CPCT]

Answer 2

Answer:

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