Let ABC be an acute triangle. Let M be the midpoint of the segment BC. Let I,J,K be the incenters of triangles ABC, ABM, ACM, respectively. Let P,Q be points on the lines MK, MJ, respectively, such that ∠AJP=∠ABC and ∠AKQ=∠BCA. Let R be the intersection of the lines CP and BQ. Prove that the lines IR and BC are perpendicular. geometry proposedgeometryincenter