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Determine the proportion TB/TA+TC/TA

Source: Romanian District Olympiad 2009, Grade IX, Problem 1

October 7, 2018
geometryvectorial geometry

Problem Statement

On the sides AB AB and AC AC of the triangle ABC ABC consider the points D, D, respectively, E, E, such that DA→+DB→+EA→+EC→=O→. \overrightarrow{DA} +\overrightarrow{DB} +\overrightarrow{EA} +\overrightarrow{EC} =\overrightarrow{O} . If T T is the intersection of DC DC and BE, BE, determine the real number α \alpha so that: TB→+TC→=α⋅TA→. \overrightarrow{TB} +\overrightarrow{TC} =\alpha\cdot\overrightarrow{TA} .
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