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The anticenter of a cyclic quadrilateral is the point where its four maltitudes
intersect. Let 
and 
be the midpoints
of the diagonals of a cyclic quadrilateral 
, and let 
be the intersection of the diagonals. Then the orthocenter
of triangle 
is the anticenter 
of 
(Honsberger 1995, p. 39).
The definition extends to a convex cyclic polygon with 
vertices.
For each pair of vertices, draw the line
perpendicular to the line segment joining them and
passing through the arithmetic mean position of
the remaining 
vertices. These generalized maltitudes
are concurrent at a point 
satisfying
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where 
is the circumcenter and 
is the arithmetic mean
position of all 
vertices (F. M. Jackson, pers. comm., Sep. 11,
2009; Mammana and Micale 2019, pp. 218-219). For 
, 
is the orthocenter of the triangle,
while 
gives the anticenter of a cyclic quadrilateral.
