The circle Ω with center O is circumscribed to acute triangle ABC. Let P be a point on the circumscribed circle of OBC, such that P is inside ABC and is different from B and C. Bisectors of angles BPA and CPA intersect the sides AB and AC in points E and F. Prove that the incenters of triangles PEF,PCA and PBA are collinear. circumcirclegeometryincenter