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在2004年全国高中数学联赛的试题中,有一道被广泛关注的选择题:设 O 点在△ABC 的内部,且+2+3=0,则△ABC 的面积与△AOC 的面积的比为( ).A.2 B3/2 C.3 D.5/3不少人对该题进行研究和推广,已公开发表的关于这方面的文章,至少有十多篇.其中,文[1]、文[2]有如下结论:’命题1(文[1]中的定理)设 O 为△ABC 所在平面上的一点,p,q,r 是不同时为0的实数,且 p+q+r=0,①则△AOB、△BOC、△AOC 的面积与△ABC 的面积之比分别为
In 2004 national high school mathematics league questions, there is a wide range of multiple-choice questions: Let O point within △ ABC, and +2 +3 = 0, then △ ABC area and △ AOC area ratio () .A.2 B3 / 2 C.3 D.5 / 3 Many people study and promote this topic, and there are at least ten articles that have been published in this field. Among them, Article [1] , [2] has the following conclusions: Proposition 1 (Theorem in [1]) Let O be a point on the plane where △ ABC is. P, q and r are real numbers that are not simultaneously 0 and p + q + r = 0, ① the area ratio of △ AOB, △ BOC, △ AOC and △ ABC are