Let cevians AA′,BB′ and CC′ of triangle ABC concur at point P. The circumcircle of triangle PA′B′ meets AC and BC at points M and N respectively, and the circumcircles of triangles PC′B′ and PA′C′ meet AC and BC for the second time respectively at points K and L. The line c passes through the midpoints of segments MN and KL. The lines a and b are defined similarly. Prove that a, b and c concur. geometrycircumcircleconcurrencyCevianmidpoints