MathDB
2016 Guts #20

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August 14, 2022
2016Guts Round

Problem Statement

Let ABCABC be a triangle such that AB=9AB=9, BC=6BC=6, and AC=10AC=10. 22 points D1,D2D_1,D_2 are labeled on BCBC such that BCBC is subdivided into 33 equal segments; 44 points E1,E2,…,E4E_1,E_2,\dots,E_4 are labeled on ACAC such that ACAC is subdivided into 55 equal segments; and 88 points F1,F2,…,F8F_1,F_2,\dots,F_8 are labeled on ABAB such that ABAB is subdivided into 99 equal segments. All possible cevians are drawn from AA to each DiD_i; from BB to each EjE_j; and from CC to each FkF_k. At how many points in the interior of △ABC\triangle ABC do at least 22 cevians intersect?
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