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.

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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.

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Related Curriculum Standards

US Common Core State Standards, Mathematics