Painting - Locus of Point on Chord (Plato)

The locus of the midpoints of the chords of a given circle that pass through a fixed point is a circle when the point lies inside of or on the circle. The small circle painted white is the locus of the midpoints of chords drawn in the large circle that pass through a point toward the top left of the inside of the circle. Three chords of the large circle are suggested. These are the diameter, whose midpoint is the center of the circle, a vertical chord through the point, and a horizontal chord through the point (only a small part of this chord is indicated). The painting is based on a diagram from College Geometry by Nathan Court. It is unclear why Crockett Johnson associated this painting with Plato.

The oil painting on masonite is #41 in the series. It has a background of two purple and gray rectangles. It has a metal and wooden frame. It shows a circle with a smaller circle inside it. The smaller circle is in two shades of white, the larger one in orange, black, gray and light purple. The painting is signed: CJ66. It is marked on the back: Crockett Johnson 1966 (/) LOCUS OF POINT ON CHORD (PLATO).

Reference: Nathan Court, College Geometry, (1964 printing), p. 13. This figure is annotated in Crockett Johnson's copy of this volume.