Let two triangle ABC and XYZ; three sidelines of ABC meet three sideline of XYZ at Ay,Az,Bx,Bz,Cy,Cz(show in the figure). Such that Ay,Az,Bx,Bz,Cy,Cz lie on a circle. A1,B1,C1,X1,Y1,Z1 respectively are circumcenter of (AAyAz),(BBxBz),(CCxCy),(XCxBx),(YAyCy),(ZAzBz). Then A1X1,B1Y1,C1Z1 are concurrent