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area of locus of symmetric points of a triangle

Source: Greece JBMO TST 1999

May 24, 2019
geometryLocusLocus problemsarea of triangleareasymmetry

Problem Statement

Φ\Phi is the union of all triangles that are symmetric of the triangle ABCABC wrt a point OO, as point OO moves along the triangle's sides. If the area of the triangle is EE, find the area of Φ\Phi.
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