MathDB
A_n is the centroid of A_{n-1}A_{n-2}A_{n-3}

Source: P8: BWM 2014

October 7, 2014
ratiogeometryperimeteranalytic geometryinductiongeometry unsolved

Problem Statement

Three non-collinear points A1,A2,A3A_1, A_2, A_3 are given in a plane. For n=4,5,6,…n = 4, 5, 6, \ldots, AnA_n be the centroid of the triangle An−3An−2An−1A_{n-3}A_{n-2}A_{n-1}.
a) Show that there is exactly one point SS, which lies in the interior of the triangle An−3An−2An−1A_{n-3}A_{n-2}A_{n-1} for all n≥4n\ge 4. b) Let TT be the intersection of the line A1A2A_1A_2 with SA3SA_3. Determine the two ratios, A1T:TA2A_1T : TA_2 and TS:SA3TS : SA_3.
Back to ProblemsView on AoPS