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find a particular set of points on a plane

Source: Romanian District Olympiad, Grade X, Problem 3

September 24, 2018
geometrycontestsOlympiadLocus problems

Problem Statement

Let α \alpha be a plane and let ABC ABC be an equilateral triangle situated on a parallel plane whose distance from α \alpha is h. h. Find the locus of the points M∈α M\in\alpha for which ∣MA∣2+h2=∣MB∣2+∣MC∣2. \left|MA\right| ^2 +h^2 = \left|MB\right|^2 +\left|MC\right|^2.
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