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Prove That: the Parallelogram, Inscribed in a Circle, is a Rectangle. - ICSE Class 10 - Mathematics

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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°) /2= 90°`
∥y, the other two angles are 90 and opposite pair of sides
Are equal.
∴ ABCD is a rectangle.

 

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Solution Prove That: the Parallelogram, Inscribed in a Circle, is a Rectangle. Concept: Arc and Chord Properties - Angle in a Semi-circle is a Right Angle.
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