在学习了《课题学习——重心》后,琪琪同学对三角形的重心很感兴趣,他很想知道“三角形三条中线相交于一点”的逻辑证明.但他却百思不得其解,于是向王老师请教.王老师先给琪琪同学讲了一个有趣的定理——燕尾定理.如图1,在△ABC中,AD,BE,CF相交于同一点O,那么S_(△ABD):S_(△ACD)=S_(△ABO):S_(△ACO)=S_(△BDO):S_(△CDO)=BD:DC.证明:分别过点A、O作AM⊥BC于点M.ON⊥BC于 After learning “Subject Learning - Focus”, Kiki students are very interested in the center of gravity of the triangle, and he would like to know the logical proof that “the three triangle intersect at one point.” However, he puzzled, So to the teacher Wang.Wang teacher first to give a lesson about the interesting theorem of Qiqi - swallowtail theorem.As shown in Figure 1, in △ ABC, AD, BE, CF intersect at the same point O, then S_ (ABD) : S ΔACD = S ΔABO: S ΔACO = S_ BDO: S ΔCDO = BD: DC. Prove that if the point A .ON⊥BC in