Question

if 2 sides of a pair of opposite sides of a cyclic quadrilateral are equal prove that its diagonal are equal


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Answer 1

Answer:

AD=BC

AC and BD are diagonals of cyclic quadrilateral.

In △AOD and △BOC

⇒ ∠OAD=∠OBC [ Same segment subtends equal angle to the circle ]

⇒ AD=BC [ Given ]

⇒ ∠ODA=∠OCB [ Same segment subtends equal angle to the circle ]

∴ △AOD≅△BOC [ By ASA congruence rule ]

Adding △DOC on both sides, we get

⇒ △AOD+△DOC≅△BOC+△DOC

⇒ △ADC≅△BCD

⇒ AC=BD [ By CPCT ]

Hence, we have proved that, a pair of opposite sides of a cyclic quadrilateral are equal prove that its diagonals are also equal