MathDB

6

Part of 2008 CentroAmerican

Problems(1)

Independent intersections

Source:

6/8/2008
Let ABC ABC be an acute triangle. Take points P P and Q Q inside AB AB and AC AC, respectively, such that BPQC BPQC is cyclic. The circumcircle of ABQ ABQ intersects BC BC again in S S and the circumcircle of APC APC intersects BC BC again in R R, PR PR and QS QS intersect again in L L. Prove that the intersection of AL AL and BC BC does not depend on the selection of P P and Q Q.
geometrycircumcircletrigonometryfunctiongeometry proposed