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Question

Prove that a parallelogram inscribed in a circle is a rectangle. [2 MARKS]

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Solution

Concept: 1 Mark
Application: 1 Mark

In the parallelogram ABCD,

A=C.....(i) (Since opposite angles of a parallelogram)

But, A+C=180 (sum of opposite angles in a cyclic quadilateral is 180)

A+A=180...... [from (i)]

2A=180

A=90

But, a parallelogram, one of whose one angle is 90, is a rectangle.

ABCD is a rectangle.


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