MathDB
PQ//BC wanted, FB = BD, DC = CE

Source: 2022 Czech-Polish-Slovak Match Junior, team p3 CPSJ

September 3, 2022
geometryparallelequal segments

Problem Statement

The points D,E,FD, E, F lie respectively on the sides BCBC, CACA, ABAB of the triangle ABC such that FB=BDF B = BD, DC=CEDC = CE, and the lines EFEF and BCBC are parallel. Tangent to the circumscribed circle of triangle DEFDEF at point FF intersects line ADAD at point PP. Perpendicular bisector of segment EFEF intersects the segment ACAC at QQ. Prove that the lines PQP Q and BCBC are parallel.
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