Re: Concurrent circles problem
- Dear Antreas,
[APH]: Let ABC be a triangle, P a point and A',B',C' the
circumcenters of PBC,PCA,PAB, resp.
The circumcircles of AB'C', BC'A', CA'B'
concur on the circumcircle of ABC, at a point, name it dP,
Which are the coordinates of dP ?
(they are somewhere in Hyacinthos, but where?)
For P = O, H we have dO = dH.
Which other isogonal conjugate points P,P*
have the same property (locus of P)?
In general, for which points P,Q we have dP = dQ ?
*** If P is not on the circumcircle, this common point dP is
the antipode of the isogonal conjugate of the infinite point of the line PP*. Equivalently, it is the perspector of the triangle bounded by the reflections of PP* in the sidelines.