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Geometric Inequality

Source: Spain Mathematical Olympiad 2018 P3

March 18, 2018
geometryinequalitiesgeometric inequalitySpain

Problem Statement

Let ABCABC be an acute-angled triangle with circumcenter OO and let MM be a point on ABAB. The circumcircle of AMOAMO intersects ACAC a second time on KK and the circumcircle of BOMBOM intersects BCBC a second time on NN.
Prove that [MNK]≥[ABC]4\left[MNK\right] \geq \frac{\left[ABC\right]}{4} and determine the equality case.
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