Let P and Q be the midpoints of non-parallel chords k1 and k2 of a circle ω, respectively. Let the tangent lines of ω passing through the endpoints of k1 intersect at A and the tangent lines passing through the endpoints of k2 intersect at B. Let the symmetric point of the orthocenter of triangle ABP with respect to the line AB be R and let the feet of the perpendiculars from R to the lines AP,BP,AQ,BQ be R1,R2,R3,R4, respectively. Prove that
PR1AR1⋅BR2PR2=QR3AR3⋅BR4QR4 geometrygeometry proposed