Explain why any parallelogram that is inscribed in a circle must be a rectangle. Draw pictures and think about properties of both cyclic quadrilaterals and parallelograms

We are talking about a cyclic quadrilateral, where the opposite angles are supplementary. Once the consecutive angles of a parallelogram are supplementary (sum = 180º) a rectangle is the only parallelogram that can be inscribed in a circle.

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ashishdwivedilVT ashishdwivedilVT · Answer 2 · 2022-04-14T16:14:13+02:00

The inscribed parallelogram should be a rectangle because a cyclic quadrilateral has a sum of opposite angles as 180°.

What is a cyclic quadrilateral?

A quadrilateral is said to be a cyclic quadrilateral if all the vertices lie on the circumference of a circle. In a cyclic quadrilateral, the sum of opposite angles is 180°.

We know that any quadrilateral that is inscribed in a circle is a cyclic quadrilateral.

In this case sum of opposite angles = 180°

We know that sum of opposite angles in a rectangle =180°

So, any parallelogram that is inscribed in a circle must be a rectangle.

Thus, The inscribed parallelogram should be a rectangle because a cyclic quadrilateral has a sum of opposite angles as 180°.

To get more about the cyclic quadrilateral visit:

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