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三角形的中心 Centres in a Triangle

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三角形的中心 Centres in a Triangle
Incenter「內心」I
- I is the intersection of the 3 angle
bisectors (角平分線) of a triangle.
triangle
- I always
lways lies inside the triangle
- I iss always the centre of the inscribed
circle (內接圓) of the △.
Circumcentre「外心」O
-
O iss the intersection of the ⊥ bisectors
(垂直平分線) of the sides of triangle
For an acute- angled(銳角
銳角)△,O lies
inside the triangle.
For a right- angled (直角
直角)△,O lies on the
hypotenuse(斜邊).
For an obtuse- angled (鈍
鈍角)△,O lies
outside the triangle.
O iss also the centre of circumcentre
circle (外接圓) of the △.
Orthocentre「垂心」H
- H iss the intersection of the 3 altitudes
(高線) (heights)) of a triangle.
- For an acute- angled(銳角
銳角)△, H lies
-
inside the triangle.
For a right- angled (直角
直角)△,H lies on
the vertex of the right angle.
For an obtuse- angled (鈍角
鈍角)△,H lies
outside the triangle.
1
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Centroid「形心」/
Centre of gravity「重心」
」G
- G iss the intersection of the 3 medians of
a triangle.
- G divides median (中線
中線) in a ratio of
2:1.
- G always lies insides the triangle.
2
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