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MathNet 2014 Question 40

Math Olympiad Vault · MathNet 2014

Question 40

The graph of the parabola $y = x^2$ is drawn on the Cartesian plane $Oxy$. The vertices of a triangle $ABC$ belong to the parabola. The median $BM$ of the triangle is parallel to the ordinate axis and is equal to $2$.
Find the area of the triangle $ABC$.