## Intersected Euler Lines

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• Let ABC be a triangle, P a point on the Euler line of ABC, and Pa,Pb,Pc the P-points of PBC,PCA,PAB, resp. (If, for example, P = O of ABC, then Oa,Ob,Oc are
Message 1 of 1 , Mar 1, 2009
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Let ABC be a triangle, P a point on the Euler line
of ABC, and Pa,Pb,Pc the P-points of PBC,PCA,PAB, resp.
(If, for example, P = O of ABC, then Oa,Ob,Oc are the O's
of PBC,PCA,PAB).

Let X(P) the inersection of the Euler lines of ABC and PaPbPc.

I am wondering for which P's the X(P) is some interesting point.

By "interesting" I mean a point with remarkable
geometric properties, or just a "simple" point
(of ABC or PaPbPc).

For example:

Let N, Na,Nb,Nc be the Nine Point Centers of:
ABC, NBC,NCA,NAB, respectively.

What point is the intersection of the Euler
Lines of ABC and NaNbNc?

Is it the Circumcenter of NaNbNc?

In other words, is the circumcenter of NaNbNc lying
on the Euler Line of ABC?

Have we discussed it before ?

APH
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