MathDB
Miklos Schweitzer 1972_8

Source:

November 5, 2008
ratiogeometryadvanced fieldsadvanced fields unsolved

Problem Statement

Given four points A1,A2,A3,A4 A_1,A_2,A_3,A_4 in the plane in such a way that A4 A_4 is the centroid of the △A1A2A3 \bigtriangleup A_1A_2A_3, find a point A5 A_5 in the plane that maximizes the ratio min⁡1≤i<j<k≤5T(AiAjAk)max⁡1≤i<j<k≤5T(AiAjAk). \frac{\min_{1 \leq i < j < k \leq 5}T(A_iA_jA_k)}{\max_{1 \leq i < j < k \leq 5}T(A_iA_jA_k)}. (T(ABC) T(ABC) denotes the area of the triangle △ABC. \bigtriangleup ABC. ) J. Suranyi
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