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Geometry with circumcircles

Source: Moscow mathematic olympiad 2022, P11.3

September 29, 2022
geometrycircumcircle

Problem Statement

Bisector ALAL is drawn in an acute triangle ABCABC. On the line LALA beyond the point AA, the point K is chosen with AK=ALAK = AL. Circumcirles of triangles BLKBLK and CLKCLK intersect segments ACAC and ABAB at points PP and QQ respectively. Prove that lines PQPQ and BCBC are parallel.