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Sum is 180

Source: Rioplatense Olympiad 2001

February 28, 2018
geometryangle bisector

Problem Statement

Let ABCABC be a acute-angled triangle with centroid GG, the angle bisector of ∠ABC\angle ABC intersects ACAC in DD. Let PP and QQ be points in BDBD where ∠PBA=∠PAB\angle PBA = \angle PAB and ∠QBC=∠QCB\angle QBC = \angle QCB. Let MM be the midpoint of QPQP, let NN be a point in the line GMGM such that GN=2GMGN = 2GM(where GG is the segment MNMN), prove that: ∠ANC+∠ABC=180\angle ANC + \angle ABC = 180
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