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MathNet 2016-part-01 — 184 problems (EN–VI) Question 108

Math Olympiad Vault · MathNet 2016-part-01 — 184 problems (EN–VI)

Question 108

A trapezoid $ABCD$ ($AB \parallel CD$) is inscribed into the parabola $y = x^2$. The line containing the midline $MN$ of this trapezoid meets the parabola at points $K$ and $L$.
Prove that the lengths of the segments $KM$ and $NL$ are equal.
(I. Gorodnin)