Locus of the Center of a Circle Inscribed in a Circular Segment

Initializing live version
Download to Desktop

Requires a Wolfram Notebook System

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

The trajectory of the center of a moving circle inscribed in a circular segment is parabolic.


This Demonstration shows this result with a horizontal chord ("base line").

Proof: Let be a circle with its center at the origin and radius with a horizontal chord given by and let be the small circle inscribed on the circular segment bounded by and . Since the circles and are tangent, the tangent point and the centers of the circles are collinear. Let be the coordinates of the center of . The radius of is equal to . Hence the distance from the origin to the center of is , which is the equation of a parabola.


Contributed by: Diego Ramos (May 2019)
Open content licensed under CC BY-NC-SA



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.