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逻辑通路/计算重心的方法
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邏輯通路
(座标平面)三角形“重心”座标公式
假设
a
→
=
B
C
→
,
b
→
=
C
A
→
,
c
→
=
A
B
→
{\displaystyle {\vec {a}}={\overrightarrow {BC}},{\vec {b}}={\overrightarrow {CA}},{\vec {c}}={\overrightarrow {AB}}}
a
=
B
C
¯
,
b
=
C
A
¯
,
c
=
A
B
¯
{\displaystyle a={\overline {BC}},b={\overline {CA}},c={\overline {AB}}}
则
重心
O
=
α
A
+
β
B
+
γ
C
α
+
β
+
γ
{\displaystyle O={\frac {\alpha A+\beta B+\gamma C}{\alpha +\beta +\gamma }}}
其中
α
=
−
a
2
(
b
→
⋅
c
→
)
β
=
−
b
2
(
c
→
⋅
a
→
)
γ
=
−
c
2
(
a
→
⋅
b
→
)
{\displaystyle {\begin{matrix}\alpha =-a^{2}({\vec {b}}\cdot {\vec {c}})\\\beta =-b^{2}({\vec {c}}\cdot {\vec {a}})\\\gamma =-c^{2}({\vec {a}}\cdot {\vec {b}})\end{matrix}}}