Kimberling’s point X(23)
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Far-out point X(23)
Let be the tangential triangle of
Let and
be the centroid, circumcircle, circumcenter, circumradius and orthocenter of
Prove that the second crosspoint of circumcircles of and
is point
Point
lies on Euler line of
Proof
Denote the inversion with respect
midpoints of
It is evident that
The inversion of circles are lines
which crosses at point
Therefore point lies on Euler line
of
as desired.
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