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Prove that it is constant

Source: Bosnia and Herzegovina TST 2010 problem 2

March 30, 2014
ratiogeometry proposedgeometry

Problem Statement

Let ABAB and FDFD be chords in circle, which does not intersect and PP point on arc ABAB which does not contain chord FDFD. Lines PFPF and PDPD intersect chord ABAB in QQ and RR. Prove that AQ∗RBQR\frac{AQ* RB}{QR} is constant, while point PP moves along the ray ABAB.
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