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balkan geo 2003

Source: Balkan MO 2003, problem 2

February 6, 2004
geometrycircumcircleratiotrapezoidtrigonometrycalculusgeometric transformation

Problem Statement

Let ABCABC be a triangle, and let the tangent to the circumcircle of the triangle ABCABC at AA meet the line BCBC at DD. The perpendicular to BCBC at BB meets the perpendicular bisector of ABAB at EE. The perpendicular to BCBC at CC meets the perpendicular bisector of ACAC at FF. Prove that the points DD, EE and FF are collinear. Valentin Vornicu
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