Two Lines Determine a Circle

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.


  • [Snapshot]
  • [Snapshot]
  • [Snapshot]


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.


    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.

Related Curriculum Standards

US Common Core State Standards, Mathematics

Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-Step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2018 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+