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Weird length conditions

Source: Latvia BW TST 2021 P12

September 26, 2021
geometrycircumcircle

Problem Statement

Five points A,B,C,P,QA,B,C,P,Q are chosen so that A,B,CA,B,C aren't collinear. The following length conditions hold: APBP=AQBQ=2120\frac{AP}{BP}=\frac{AQ}{BQ}=\frac{21}{20} and BPCP=BQCQ=2019\frac{BP}{CP}=\frac{BQ}{CQ}=\frac{20}{19}. Prove that line PQPQ goes through the circumcentre of △ABC\triangle ABC.
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