Maltitude
Maltitude
A maltitude ("midpoint altitude") is a perpendicular drawn to a side of a quadrilateral from the midpoint M_i of the opposite side.
MaltitudesCyclic
If the quadrilateral is cyclic, then the maltitudes are concurrent in a point T known as the anticenter. Amazingly, in addition, the centroid G of the quadrilateral vertices is exactly the midpoint of the line connecting T and the quadrilateral's circumcenter O.
See also
Altitude, Anticenter, Brahmagupta's Theorem, Cyclic Quadrilateral, Midpoint, QuadrilateralExplore with Wolfram|Alpha
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References
Honsberger, R. Episodes in Nineteenth and Twentieth Century Euclidean Geometry. Washington, DC: Math. Assoc. Amer., pp. 36-37, 1995.Wells, D. The Penguin Dictionary of Curious and Interesting Geometry. London: Penguin, p. 146, 1991.Referenced on Wolfram|Alpha
MaltitudeCite this as:
Weisstein, Eric W. "Maltitude." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Maltitude.html