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Part of 1981 Bundeswettbewerb Mathematik

Problems(2)

Bundeswettbewerb Mathematik 1981 Problem 1.2

Source: Bundeswettbewerb Mathematik 1981 Round 1

Prove that if the sides

a, b, c

of a non-equilateral triangle satisfy

a + b = 2c

, then the line passing through the incenter and centroid is parallel to one of the sides of the triangle.

geometryClassicCentroidparallel

A bijective mapping

Source:

A bijective mapping from a plane to itself maps every circle to a circle. Prove that it maps every line to a line.

geometry unsolvedgeometry