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MathNet 2014 Question 99

Math Olympiad Vault · MathNet 2014

Question 99

Three points $A$, $B$ and $C$ are considered on a parabola. The tangents to the parabola at these points form a triangle $KLM$ ($KL$ being tangent at $A$, $KM$ at $B$, and $LM$ at $C$). The line through $B$ parallel to the axis of symmetry of the parabola intersects $AC$ at $N$. Prove that $KLMN$ is a parallelogram.

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