Two Lines Determine a Circle

Requires a Wolfram Notebook System

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

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



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.

Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.