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