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If a pair of opposite side of a cyclic quadrilateral are equal prove that its diagonal are also equal

Posted by Deepanshu Pandey 4 years, 9 months ago

CBSE > Class 09 > Mathematics

1 answers

Yogita Ingle 4 years, 9 months ago

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

Hence, when pair of opposite sides of a cyclic quadrilateral are equal, diagonals are also equal.

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