In-centre: Point of intersection of the three angle bisectors of a triangle
內心：一個三角形的三條角平分線的交點
Acute-angled triangle
Obtuse-angled triangle
Right-angled triangle
銳角三角形
鈍角三角形
直角三角形
B
B
B
in-centre
in-centre
in-centre
I
A
I
A
C
I
A
C
C
Centroid: Point of intersection of the three medians of a triangle
形心：一個三角形的三條中線的交點
Acute-angled triangle
Obtuse-angled triangle
Right-angled triangle
銳角三角形
鈍角三角形
直角三角形
B
centroid
R
P
Q
centroid
R
P
P
G
G
G
A
B
B
centroid
R
C
A
Q
C
A
Q
C
Circumcentre: Point of intersection of the three perpendicular bisectors of a triangle
外心：一個三角形的三條垂直平分線的交點
Acute-angled triangle
Obtuse-angled triangle
Right-angled triangle
銳角三角形
鈍角三角形
直角三角形
B
B
circumcentre
circumcentre
O
O
O
A
C
A
C
circumcentre
The circumcentre lies
inside the triangle.
B
A
C
The circumcentre lies at
the mid-point of the
hypotenuse.
The circumcentre lies
outside the triangle.
Orthocentre: Point of intersection of the three altitudes of a triangle
垂心：一個三角形的三條頂垂線的交點
Acute-angled triangle
Obtuse-angled triangle
Right-angled triangle
銳角三角形
鈍角三角形
直角三角形
orthocentre B
B
A
H
C
A
The orthocentre lies
inside the triangle.
B
C
orthocentre
The orthocentre lies
outside the triangle.
H
A
orthocentre
C
The orthocentre lies on a
vertex of the triangle.