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Isosceles triangle

Source: Middle European Mathematical Olympiad 2013 I-3

May 17, 2014
geometryperpendicular bisectorgeometry proposedanglechasing

Problem Statement

Let ABCABC be an isosceles triangle with AC=BCAC=BC. Let NN be a point inside the triangle such that 2∠ANB=180∘+∠ACB2 \angle ANB = 180 ^\circ + \angle ACB . Let D D be the intersection of the line BNBN and the line parallel to ANAN that passes through CC. Let PP be the intersection of the angle bisectors of the angles CANCAN and ABNABN. Show that the lines DPDP and ANAN are perpendicular.
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