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Distance between the Centers of the Nine-Point and Apollonius Circles
For a triangle
, let
and
be the circumradius and inradius,
be the semiperimeter,
b
e the nine-point circle and
be the Apollonius circle.
Then
,
,
and
.
You can drag the points
,
and
.
Contributed by:
Minh Trinh Xuan
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RELATED LINKS
A Triangle Formed by the Centers of Three Nine-Point Circles
(
Wolfram Demonstrations Project
)
Nine-Point Circle
(
Wolfram Demonstrations Project
)
Nine-Point Center
(
Wolfram
MathWorld
)
Nine-Point Circle in the Complex Plane
(
Wolfram Demonstrations Project
)
Apollonius Circle
(
Wolfram
MathWorld
)
Radical Circle of Three Circles
(
Wolfram Demonstrations Project
)
Tetrahedron Centers
(
Wolfram Demonstrations Project
)
The Center and Radius of the Nine-Point Circle
(
Wolfram Demonstrations Project
)
PERMANENT CITATION
Minh Trinh Xuan
"
Distance between the Centers of the Nine-Point and Apollonius Circles
"
http://demonstrations.wolfram.com/DistanceBetweenTheCentersOfTheNinePointAndApolloniusCircles/
Wolfram Demonstrations Project
Published: June 7, 2022
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