MathDB

Five points

A,B,C,P,Q

are chosen so that

A,B,C

aren't collinear. The following length conditions hold:

\frac{AP}{BP}=\frac{AQ}{BQ}=\frac{21}{20}

and

\frac{BP}{CP}=\frac{BQ}{CQ}=\frac{20}{19}

. Prove that line

PQ

goes through the circumcentre of

\triangle ABC

P12