In geometry, the midpoint theorem describes a property of parallel chords in a conic. It states that the midpoints of parallel chords in a conic are located on a common line.
The common line or line segment for the midpoints is called the diameter. For a circle, ellipse or hyperbola the diameter goes through its center. For a parabola the diameter is always perpendicular to its directrix and for a pair of intersecting lines (from a degenerate conic) the diameter goes through the point of intersection.
Gallery ( = eccentricity):
References David Alexander Brannan, Matthew F. Esplen, Jeremy J. Gray (1999) Geometry Cambridge University Press , pages 59–66 Aleksander Simonic (November 2012) "On a Problem Concerning Two Conics", Crux Mathematicorum, volume 38(9): 372–377 C. G. Gibson (2003) Elementary Euclidean Geometry: An Introduction. Cambridge University Press pages 65–68
External links Locus of Midpoints of Parallel Chords of Central Conic passes through Center at the Proof Wiki midpoints of parallel chords in conics lie on a common line - interactive illustration