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Question
Prove that, any rectangle is a cyclic quadrilateral.
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Solution
Suppose ABCD is a rectangle.
∴ ∠A = ∠B = ∠C = ∠D = 90º (Each angle of a rectangle is 90º)
⇒ ∠A + ∠C = 180º and ∠B + ∠D = 180º
We know, if a pair of opposite angles of a quadrilateral is supplementary, then quadrilateral is cyclic.
∴ Rectangle ABCD is a cyclic quadrilateral.
So, any rectangle is a cyclic quadrilateral.
Suppose ABCD is a rectangle.
∴ ∠A = ∠B = ∠C = ∠D = 90º (Each angle of a rectangle is 90º)
⇒ ∠A + ∠C = 180º and ∠B + ∠D = 180º
We know, if a pair of opposite angles of a quadrilateral is supplementary, then quadrilateral is cyclic.
∴ Rectangle ABCD is a cyclic quadrilateral.
So, any rectangle is a cyclic quadrilateral.
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