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Question

Prove that, any rectangle is a cyclic quadrilateral.


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.
 

Mathematics
Mathematics Part - II (Solutions)
Standard X

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