[Antreas P. Hatzipolakis]:
Let ABC be a triangle and A'B'C' the pedal triangle of I.
Denote:
(Na), (Nb), (Nc) = the NPCs of IBC, ICA, IAB, resp.
A", B", C" = the antipodes of A', B', C' in (Na), (Nb), (Nc), resp.
The circumcircles of IA'A", IB'B", IC'C" are coaxial.
2nd, other than I, intersection?
Denote:
(Na), (Nb), (Nc) = the NPCs of IBC, ICA, IAB, resp.
A", B", C" = the antipodes of A', B', C' in (Na), (Nb), (Nc), resp.
The circumcircles of IA'A", IB'B", IC'C" are coaxial.
2nd, other than I, intersection?
[Peter Moses]:
Hi Antreas,
a (a^2-b^2-c^2) (2 a^7-a^6 b-4 a^5 b^2+a^4 b^3+2 a^3 b^4+a^2 b^5-b^7-a^6 c+8 a^5 b c-a^4 b^2 c-4 a^3 b^3 c+a^2 b^4 c-4 a b^5 c+b^6 c-4 a^5 c^2-a^4 b c^2+4 a^3 b^2 c^2-2 a^2 b^3 c^2+3 b^5 c^2+a^4 c^3-4 a^3 b c^3-2 a^2 b^2 c^3+8 a b^3 c^3-3 b^4 c^3+2 a^3 c^4+a^2 b c^4-3 b^3 c^4+a^2 c^5-4 a b c^5+3 b^2 c^5+b c^6-c^7)::
on the cubic K825 and these lines: {{1,84},{517,1295},{521,656},{971,15500},{1259,6617},{1319,1364},{1439,14878},{1785,6357},{3057,7335},{6259,7952}}.
incircle inverse of X(1071).
Conway circle inverse of X(12547).
crossdifference of every pair of points on line X(19) X(14298).
a (a^2-b^2-c^2) (2 a^7-a^6 b-4 a^5 b^2+a^4 b^3+2 a^3 b^4+a^2 b^5-b^7-a^6 c+8 a^5 b c-a^4 b^2 c-4 a^3 b^3 c+a^2 b^4 c-4 a b^5 c+b^6 c-4 a^5 c^2-a^4 b c^2+4 a^3 b^2 c^2-2 a^2 b^3 c^2+3 b^5 c^2+a^4 c^3-4 a^3 b c^3-2 a^2 b^2 c^3+8 a b^3 c^3-3 b^4 c^3+2 a^3 c^4+a^2 b c^4-3 b^3 c^4+a^2 c^5-4 a b c^5+3 b^2 c^5+b c^6-c^7)::
on the cubic K825 and these lines: {{1,84},{517,1295},{521,656},{971,15500},{1259,6617},{1319,1364},{1439,14878},{1785,6357},{3057,7335},{6259,7952}}.
incircle inverse of X(1071).
Conway circle inverse of X(12547).
crossdifference of every pair of points on line X(19) X(14298).
Best regards,
Peter Moses.
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