Thứ Sáu, 12 tháng 9, 2014

10-Another seven circle theorem

Let two triangle \triangle ABC and \triangle XYZ; three sidelines of \triangle XYZ meet three sideline of \triangle ABC at A_y,A_z,B_x,B_z,C_y,C_z(show in the figure). Such that A_y,A_z,B_x,B_z,C_y,C_x lie on a circle. A_1,B_1,C_1,X_1,Y_1,Z_1 respectively are circumcenter of (AA_yA_z),(BB_xB_z)(CC_xC_y),(XC_xB_x),(YA_yC_y),(ZA_zB_z).  Prove that A_1X_1,B_1Y_1,C_1Z_1 are concurrent


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