Kimberling’s point X(23)
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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