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Four Centers of a Triangle (part I)
© Copyright 2000, Jim Loy
This interactively demonstrates that certain lines which are related to
a triangle intersect in one point. Move the bright red dot to change the shape
of the four triangles, and see these lines continue to intersect. These four
triangles show:
- Circumcenter (upper left): The perpendicular bisectors of the three
sides meet at the circumcenter. This point is the center of the circle (called
the circumcircle) that circumscribes the triangle.
- Incenter (upper right): The bisectors of the angles meet at the
incenter. This point is the center of the circle (called the incircle) that
inscribes the triangle.
- Centroid (lower left): The lines connecting the vertices with the
midpoint of the opposite sides meet at the centroid. This point is the center
of gravity of the triangle if it is made of a uniform material.
- Orthocenter (lower right): The three altitudes meet at the
orthocenter.
See Four Centers of a Triangle (part II). Also
see The Centers of a Triangle for more
information.
The above Java interactive demonstration was created with
Cinderella (a geometry program).
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