MathDB

3

Part of 2018 Spain Mathematical Olympiad

Problems(1)

Geometric Inequality

Source: Spain Mathematical Olympiad 2018 P3

3/18/2018
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.
geometryinequalitiesgeometric inequalitySpain