Let AB and FD be chords in circle, which does not intersect and P point on arc AB which does not contain chord FD. Lines PF and PD intersect chord AB in Q and R. Prove that AQ∗RBQR is constant, while point P moves along the ray AB.
Source: Bosnia and Herzegovina TST 2010 problem 2
Tags: ratio, geometry proposed, geometry
Let AB and FD be chords in circle, which does not intersect and P point on arc AB which does not contain chord FD. Lines PF and PD intersect chord AB in Q and R. Prove that AQ∗RBQR is constant, while point P moves along the ray AB.