Given a circle and a point K inside it. An arbitrary circle equal to the given one and passing through the point K has a common chord with the given circle. Find the geometric locus of the midpoints of these chords.
Can't prove it but my guess just from sketching on paper is that these points form a circle, centered on the midpoint between K and the center of the original circle, with a radius half that of the original circle.
e.g. if you have a circle with radius 10 centered on the origin, and place K at (6,0), you end up with a circle of radius 5 centered at (3,0).
Posted by tomarken
on 2021-04-30 08:55:38