Interactive resource
Homothety locus (“melon–bean”)
Geometry. Driver on a circle; follower at fixed ratio about A also traces a circle. Free interactive GeoGebra resource — adjust parameters in the browser.
Overview
Driver on a circle; follower at fixed ratio about A also traces a circle.
Explanation
If driver P moves on a circle and follower Q satisfies AQ/AP = k (homothety about A),
then Q’s locus is also a circle (radius scaled by |k|).
Memory aid: if the driver traces a circle, so does the follower under homothety.
How to use
Drag P around the circle; Q on ray AP traces the dashed smaller circle.