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

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Question

Prove that:
the rhombus, inscribed in a circle, is a square.

Solution

 

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
are equal.
∴ ABCD is a square.

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