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幼苗
共回答了15个问题采纳率:93.3% 举报
由于→OA = →OG + →GA ==> (OA)^2 = (→OG + →GA)^2 = (OG)^2 + (GA)^2 + 2*(→OG)*(→GA) ==> OA^2 + OB^2 + OC^2 = GA^2 + GB^2 + GC^2 + 3OG^2 + 2*(→OG)*(→GA + →GB + →GC) 只需证明→GA + →GB + →GC = 0 假设A(x1,y1),B(x2,y2),C(x3,y3),则由于G是重心,有:x(G) = (x1 + x2 + x3)/3,y(G) = (y1 + y2 + y3)/3 ==> →GA = [ x1 - (x1 + x2 + x3)/3,y1 - (x1 + x2 + x3)/3 ] 其它也类似,因此有:→GA + →GB + →GC = 0
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1年前
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