9170Re: [EMHL] Orthologic Triangles
- Feb 1, 2004Dear Antreas, Fred and Darij
> Let ABC be a triangle, P a point, and (Oa, Ob, Oc)Consider three lines La, Lb, Lc going respectively through A, B, C
> the Circumcenters of the triangles PBC, PCA, PAB, resp.
> The locus of P such that the perpendiculars
> from A,B,C to POa, POb, POc are concurrent is:
> infinity line*circumcircle*KjP cubic.
and such as (La,POa) = (Lb,POb) = (Lc,POc) = phi where (L1,L2) is
the measure modulo Pi of the oriented angle of lines L1, L2.
Then La, Lb, Lc concur if and only if
(AP,BC)+(BP,CA)+(CP,AB) = Pi/2-phi
Thus, we get the MacCay cubic for phi = 0, the Kjp cubic for phi =
Pi/2 and, for any theta, a member of the pencil generated by Kjp and
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