证明:
OP=1/2OA+1/3OB+(1-1/2-1/3)OC
=1/2OA-1/2OC+1/3OB-1/3OC+OC
=1/2(OA-OC)+1/3(OB-OC)+OC
=1/2CA+1/3CB+OC
等价于:OP-OC=1/2CA+1/3CB
∴ CP=1/2CA+1/3CB
∴四点共面
证明:
OP=1/2OA+1/3OB+(1-1/2-1/3)OC
=1/2OA-1/2OC+1/3OB-1/3OC+OC
=1/2(OA-OC)+1/3(OB-OC)+OC
=1/2CA+1/3CB+OC
等价于:OP-OC=1/2CA+1/3CB
∴ CP=1/2CA+1/3CB
∴四点共面