O为三角形ABC的内切圆的圆心,a.b.c为角A,角B 角C所对的边的边长,求证:a向量OA+b向量OB+c向量OC=0O为三角形ABC的内切圆的圆心,a.b.c为角A,角B 角C所对的边的边长,求证:a乘以向量OA+b乘以向量OB+c乘
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O为三角形ABC的内切圆的圆心,a.b.c为角A,角B 角C所对的边的边长,求证:a向量OA+b向量OB+c向量OC=0O为三角形ABC的内切圆的圆心,a.b.c为角A,角B 角C所对的边的边长,求证:a乘以向量OA+b乘以向量OB+c乘
O为三角形ABC的内切圆的圆心,a.b.c为角A,角B 角C所对的边的边长,求证:a向量OA+b向量OB+c向量OC=0
O为三角形ABC的内切圆的圆心,a.b.c为角A,角B 角C所对的边的边长,求证:a乘以向量OA+b乘以向量OB+c乘以向量OC=0
O为三角形ABC的内切圆的圆心,a.b.c为角A,角B 角C所对的边的边长,求证:a向量OA+b向量OB+c向量OC=0O为三角形ABC的内切圆的圆心,a.b.c为角A,角B 角C所对的边的边长,求证:a乘以向量OA+b乘以向量OB+c乘
证明:
a=OB-OC
b=OC-OA
c=OA-OB
则a*OA+b*OB+c*OC=(OB-OC)*OA+(OC-OA)*OB+(OA-OB)*OC
展开即可得证!