MathDB
Independent intersections

Source:

June 8, 2008
geometrycircumcircletrigonometryfunctiongeometry proposed

Problem Statement

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.
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