文[1]提出三角形的一个性质如下:性质已知△ABC及其内部一点P,若λ1PA+λ2PB+λ3PC=0,λ1,λ2,λ3都是大于0的实数,则△PBC,△PAC,△PAB的面积之比为λ1∶λ2∶λ3.(即S△PBC∶S△PAC∶S△PAB=λ1∶λ2∶λ3)文[1]提供的证法较繁,本文将提供一种较简单的证法.证明要证明性质成 A property of the triangle proposed in [1] is as follows: The property is known as △ABC and its internal point P. If λ1PA+λ2PB+λ3PC=0, λ1, λ2 and λ3 are all real numbers greater than 0, then △PBC, △PAC, The area ratio of △ PAB is λ1 : λ2 : λ3. (that is S △ PBC : S PAC PAC : S PA PAB = λ1 : λ2 : λ3). The proving method provided in [1] is more complicated. This article will provide a comparison. Simple proof. Prove to prove nature