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A, D, N are collinear iff BAC = 45º

Source: Problem 1, Brazilian MO 2015

October 20, 2015
geometry proposedgeometrycircumcircle

Problem Statement

Let △ABC\triangle ABC be an acute-scalene triangle, and let NN be the center of the circle wich pass trough the feet of altitudes. Let DD be the intersection of tangents to the circumcircle of △ABC\triangle ABC at BB and CC. Prove that AA, DD and NN are collinear iff ∡BAC=45º\measuredangle BAC = 45º.
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