# Finding the Diameter of a Cyclic Quadrilateral

• schlynn
In summary, a cyclic quadrilateral is a four-sided figure where all four vertices lie on a single circle. The diameter of a cyclic quadrilateral can be found by connecting the midpoints of the sides to form a smaller quadrilateral, and the relationship between the diameter and the sides is equal to the product of the diagonals divided by the sum of the sides. There is a formula for finding the diameter of a cyclic quadrilateral, and it can have more than one diameter due to the possibility of forming two smaller quadrilaterals with different diagonals.
schlynn

## Homework Statement

Given a cyclic quadrilateral with side lengths 1, 2, 3 and d (in that order) where d is the diameter of the circle, find d.

## The Attempt at a Solution

I tried using Ptolemy's theorem and Brahmagupta's formula, but to no avail. Can I get pointed in the correct direction please?

Maybe you can find something useful http://pballew.blogspot.com/2009/10/notes-on-cyclic-quadrilaterals.html" .

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## What is a cyclic quadrilateral?

A cyclic quadrilateral is a four-sided figure where all four vertices lie on a single circle.

## How do you find the diameter of a cyclic quadrilateral?

The diameter of a cyclic quadrilateral can be found by connecting the midpoints of the sides of the quadrilateral to form a smaller quadrilateral. The diameter of the original quadrilateral is then equal to the diagonal of the smaller quadrilateral.

## What is the relationship between the diameter and the sides of a cyclic quadrilateral?

The diameter of a cyclic quadrilateral is equal to the product of the diagonals divided by the sum of the sides.

## Is there a formula for finding the diameter of a cyclic quadrilateral?

Yes, the formula for finding the diameter of a cyclic quadrilateral is: d = (ab + cd) / (a + c), where a and c are the lengths of opposite sides and b and d are the lengths of the remaining sides.

## Can a cyclic quadrilateral have more than one diameter?

Yes, a cyclic quadrilateral can have two diameters, as the midpoints of the sides can form two smaller quadrilaterals with different diagonals, both of which can be considered as diameters of the original quadrilateral.

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