MathDB
"Isotomic" triangles have equal areas

Source: classical; e. g.: [apparently Arthur] Engel, Praxis der Mathematik problem P144; used in 4th QEDMO

November 10, 2007
geometrygeometric transformationreflection3D geometryprismgeometry theorems

Problem Statement

Let ABC ABC be a triangle, and let X X, Y Y, Z Z be three points on the segments BC BC, CA CA, AB AB, respectively. Denote by X′ X^{\prime}, Y′ Y^{\prime}, Z′ Z^{\prime} the reflections of these points X X, Y Y, Z Z in the midpoints of the segments BC BC, CA CA, AB AB, respectively. Prove that \left\vert XYZ\right\vert \equal{}\left\vert X^{\prime}Y^{\prime}Z^{\prime}\right\vert.
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