Question

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

It's pretty urgent .
[ Answer as per Circles , class 9 ]

Answer 1

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Answer 2

Hey!!

Here is your required answer :D


In the given fig.,

We, have to prove AC = BD
First, we have to do construction, Join AC & BD.

∴ In ΔAOD and ΔBOC

     ∠ODA = ∠OCB { ∵  Angles in the same segment of a circle are equal }
     ∠OAD = ∠OBC { ∵  Angles in the same segment of a circle are equal }

Now, ΔAOD = ΔBOC {by ASA criteria}

So, Adding DOC on both sides, We obtain
=)  ΔAOD+ ΔDOC ≅ ΔBOC + ΔDOC
=) ΔADC ≅ ΔBCD

∴ AC = BD {by Corresponding parts of Congruent Triangles}


Hope it helps you ^_^