MathDB
[JKL] >= [ABC], lines of medians and circumcircle

Source: Canada Repêchage 2023/6 CMOQR

March 25, 2024
geometryareasgeometric inequalitycircumcircle

Problem Statement

Given triangle ABCABC with circumcircle Γ\Gamma, let DD, EE, and FF be the midpoints of sides BCBC, CACA, and ABAB, respectively, and let the lines ADAD, BEBE, and CFCF intersect Γ\Gamma again at points JJ, KK, and LL, respectively. Show that the area of triangle JKLJKL is at least that of triangle ABCABC.
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