Kimberling’s point X(25)
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PERSPECTOR OF ORTHIC AND TANGENTIAL TRIANGLES X(25)
Let be the orthic triangle of
Let
be the circumcenter of
Let
be the tangencial triangle of
Let
be the circumcenter of
Prove that lines and
are concurrent at point, lies on Euler line of
Proof
and
are antiparallel to BC with respect
Similarly,
Therefore homothetic center of
and
is the point of concurrence of lines
and
Denote this point as
The points and
are the corresponding points (circumcenters) of
and
so point
lies on line
Points and
lies on Euler line, so
lies on Euler line of
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