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Question
Prove that the parallelogram, inscribed in a circle, is a rectangle.
Solution
Let ABCD be a parallelogram, inscribe in a circle,
Now, ∠BAD + ∠BCD
(Opposite angles of a parallelogram are equal)
And ∠BAD + ∠BCD = 180°
(Pair of opposite angles in a cyclic quadrilateral are supplementary)
∠BAD + ∠BCD = `(180^circ)/2` = 90°
The other two angles are 90° and opposite pair of sides are equal.
∴ ABCD is a rectangle.
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