MEMO 2015 ekipno problem 6


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28. kolovoza 2018.
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Let I be the incentre of triangle ABC with |AB| > |AC| and let the line AI intersect the side BC at D. Suppose that point P lies on the segment BC and satisfies |PI| = |PD|. Further, let J be the point obtained by reflecting I over the perpendicular bisector of BC, and let Q be the other intersection of the circumcircles of the triangles ABC and APD. Prove that |\angle{BAQ}| = |\angle{CAJ}|.

Izvor: Srednjoeuropska matematička olimpijada 2015, ekipno natjecanje, problem 6