Q.

If a circle can be inscribed in a parallelogram how will the parallelogram change?

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Detailed Solution

If a circle can be inscribed in a parallelogram it will be a rectangle.

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Let ABCD be a parallelogram inscribed in a circle.
Opposite angles of a parallelogram are equal

So ∠𝐡A𝐷 = ∠𝐡𝐢𝐷

Pair of opposite angles in a cyclic quadrilateral are supplementary ∠𝐡A𝐷 = ∠𝐡𝐢𝐷

=180∘2=90∘

Similarly the other two angles are also 90Β° and opposite pair of sides are equal
Therefore, 𝐴𝐡𝐢𝐷 is a rectangle.

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