# On the number of maximum-area triangles in a planar graph

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Peter Braß

Institut für Informatik

Freie Universität Berlin

Takustr. 9, D-14195 Berlin

email: brass@inf.fu-berlin.de

Report B 99-07

April 1999

In this note we prove that in a set of *n* points in the plane, not all on a line, the maximum area of a triangle is reached by at most *n* of the $\{n\choose 3}$ triangles determined by these points, and this number of maximum-area triangles is reached by several constructions. This answers a question of Erdös and Purdy of 1971.

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