the rhombus, inscribed in a circle, is a square.
Let ABCD be a rhombus, inscribed 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 all the sides
∴ ABCD is a square.
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