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Inequality for a Cevian Involving the Circumradius
Let
be a triangle; define
,
,
and let
be the circumcircle of
.
For a point
, let
,
,
be signed areas and set
, the barycentric coordinates of
, so that
.
Let
.
Then
, with equality if and only if
is on
.
You can drag the vertices
,
,
.
Contributed by:
Minh Trinh Xuan
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RELATED LINKS
Cevian
(
Wolfram
MathWorld
)
Inequalities for an Exradius of a Triangle
(
Wolfram Demonstrations Project
)
An Inequality for Tripolar Coordinates Related to the Brocard Angle
(
Wolfram Demonstrations Project
)
Radical Circle of Three Circles
(
Wolfram Demonstrations Project
)
BarycentricCoordinates
(
Wolfram web resource
)
PERMANENT CITATION
Minh Trinh Xuan
"
Inequality for a Cevian Involving the Circumradius
"
http://demonstrations.wolfram.com/InequalityForACevianInvolvingTheCircumradius/
Wolfram Demonstrations Project
Published: June 15, 2022
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