# Two Lines Determine a Circle

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram CDF Player or other Wolfram Language products.

Requires a Wolfram Notebook System

Edit on desktop, mobile and cloud with any Wolfram Language product.

Two lines rotate at the same speed around separate centers. Surprisingly, their intersection always outlines a circle that passes through the two pivot points. Their phase relation, indicated by the blue wedge, determines the size of the circle. A 90 degree offset puts the two pivot points at each end of a diameter.

Contributed by: John Kiehl (March 2011)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

To understand why this phenomenon is so, notice that the light blue point of intersection goes around the circle *twice* for every single 360° rotation of the lines. This is just another way of observing that the central angle of an arc of a circle is twice any angle drawn from *any* point on the circle itself. The two red pivot points can now be seen as two such points on a circle.

## Permanent Citation

"Two Lines Determine a Circle"

http://demonstrations.wolfram.com/TwoLinesDetermineACircle/

Wolfram Demonstrations Project

Published: March 7 2011