Question
Prove that:
the parallelogram, inscribed in a circle, is a rectangle.
the parallelogram, inscribed in a circle, is a rectangle.
✓
Answer
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)
$\angle BAD =\angle BCD =\frac{180^{\circ}}{2}=90^{\circ}$
∥y, the other two angles are 90 and opposite pair of sides
Are equal.
∴ ABCD is a rectangle.
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