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parallel wanted, tangents at circumcircle related

Source: 2015 Moldova JBMO TST 1.3

July 11, 2020
geometrycircumcircleTangentsparallel

Problem Statement

Let Ω\Omega be the circle circumscribed to the triangle ABCABC. Tangents taken to the circle Ω\Omega at points AA and BB intersects at the point PP , and the perpendicular bisector of (BC) (BC) cuts line ACAC at point QQ. Prove that lines BCBC and PQPQ are parallel.
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