MathDB
Upper bound k for least area of triangle with segment MN

Source: Romanian TST 2002

February 5, 2011
geometrysymmetrycombinatorics proposedcombinatorics

Problem Statement

Let ABCDABCD be a unit square. For any interior points M,NM,N such that the line MNMN does not contain a vertex of the square, we denote by s(M,N)s(M,N) the least area of the triangles having their vertices in the set of points {A,B,C,D,M,N}\{ A,B,C,D,M,N\}. Find the least number kk such that s(M,N)≤ks(M,N)\le k, for all points M,NM,N.
Dinu Șerbănescu
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