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A Concurrence Based on Ellipses through the Incenter
Let
be the incenter of a triangle
. A point
satisfies the conditions
,
. The points
and
are defined analogously. Then the lines extended from
,
and
intersect at the red point.
Contributed by:
HongYang Cao
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References
[1] Colescu. "An Interesting Geometry Problem about Incenter and Ellipses." (Jan 9, 2020)
math.stackexchange.com/questions/1897127/an-interesting-geometry-problem-about-incenter-and-ellipses
.
[2] I. I. Bogdanov, "Two Theorems on the Focus-Sharing Ellipses: A Three-Dimensional View,"
Journal of Classical Geometry
,
1
, 2012 pp. 1–5.
jcgeometry.org/Articles/Volume1/JCG2012V1pp1-5.pdf
.
[3] S. Liebscher and D.-E. Liebscher, "The Love for the Three Conics,"
Forum Geometricorum
,
18
, 2018 pp. 419–430.
forumgeom.fau.edu/FG2018volume18/FG201848.pdf
.
RELATED LINKS
A Concurrency from the Reflection of the Incircle's Contact Points across the Incenter
(
Wolfram Demonstrations Project
)
PERMANENT CITATION
HongYang Cao
"
A Concurrence Based on Ellipses through the Incenter
"
http://demonstrations.wolfram.com/AConcurrenceBasedOnEllipsesThroughTheIncenter/
Wolfram Demonstrations Project
Published: February 18, 2020
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