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Squares drawn outwardly of ABC

Source: Federation of Bosnia, 1. Grades 2008.

April 23, 2008

geometryparallelogramanalytic geometryvectorcomplex numbers

Problem Statement

Squares

BCA_{1}A_{2}

CAB_{1}B_{2}

ABC_{1}C_{2}

are outwardly drawn on sides of triangle

\triangle ABC

. If

AB_{1}A'C_{2}

BC_{1}B'A_{2}

CA_{1}C'B_{2}

are parallelograms then prove that: (i) Lines

BC

and

AA'

are orthogonal. (ii)Triangles

\triangle ABC

and

\triangle A'B'C'

have common centroid