[Antreas P. Hatzipolakis]:
Let ABC be a triangle and A'B'C' the pedal triangle of I.
Denote:
[Angel Montesdeoca]:
1. The NPCs of IGeA', IGeB', IGeC' are coaxial the 2nd, other than midpoint of IGe, intersection is X(5083) = X(125)-of-intouch-triangle.
2. The NPCs of IGeA", IGeB", IGeC" are coaxial, the 2nd, other than midpoint of IGe, intersection is
W = (a+b-c) (a-b+c) (4 a^10
-a^9 (b+c)+4 a^8 (9 b^2-26 b c+9 c^2)
+a^7 (-354 b^3+361 b^2 c+361 b c^2-354 c^3)
+2 a^6 (465 b^4-76 b^3 c-750 b^2 c^2-76 b c^3+465 c^4)
-a^5 (1044 b^5+827 b^4 c-1851 b^3 c^2-1851 b^2 c^3+827 b c^4+1044 c^5)
+2 a^4 (b-c)^2 (213 b^4+1073 b^3 c+1680 b^2 c^2+1073 b c^3+213 c^4)
+a^3 (b-c)^2 (114 b^5-365 b^4 c-1549 b^3 c^2-1549 b^2 c^3-365 b c^4+114 c^5)
-2 a^2 (b-c)^4 (63 b^4+286 b^3 c+490 b^2 c^2+286 b c^3+63 c^4)
+5 a (b-c)^4 (b^5+24 b^4 c+83 b^3 c^2+83 b^2 c^3+24 b c^4+c^5)
+2 (b-c)^6 (5 b^4+25 b^3 c+48 b^2 c^2+25 b c^3+5 c^4)) : ... : ....
W lies on the line: {3321,5542}
Denote:
Ge = Gergonne point X(7) ie the point the AA', BB', CC' are concurrent at.
A" = the other than A' intersection of AA' and the incircle
A" = the other than A' intersection of AA' and the incircle
B" = the other than B' intersection of BB' and the incircle
C" = the other than C' intersection of CC' and the incircle
1. The NPCs of IGeA', IGeB', IGeC' are coaxial
2. The NPCs of IGeA", IGeB", IGeC" are coaxial
2nd, other than midpoint of IGe, intersections?
****************************** ***************************
Let ABC be a triangle
Denote:
2. The NPCs of IGeA", IGeB", IGeC" are coaxial
2nd, other than midpoint of IGe, intersections?
****************************** ***************************
Let ABC be a triangle
Denote:
A', B', C' = the reflections of I in BC, CA, AB, resp.
D = the point X(79) ie the point the AA', BB', CC' are concurrent at.
3. The NPCs of IDA', IDB', IDC' are coaxial
2nd, other than midpoint of ID, intersection?
2nd, other than midpoint of ID, intersection?
[Angel Montesdeoca]:
1. The NPCs of IGeA', IGeB', IGeC' are coaxial the 2nd, other than midpoint of IGe, intersection is X(5083) = X(125)-of-intouch-triangle.
2. The NPCs of IGeA", IGeB", IGeC" are coaxial, the 2nd, other than midpoint of IGe, intersection is
W = (a+b-c) (a-b+c) (4 a^10
-a^9 (b+c)+4 a^8 (9 b^2-26 b c+9 c^2)
+a^7 (-354 b^3+361 b^2 c+361 b c^2-354 c^3)
+2 a^6 (465 b^4-76 b^3 c-750 b^2 c^2-76 b c^3+465 c^4)
-a^5 (1044 b^5+827 b^4 c-1851 b^3 c^2-1851 b^2 c^3+827 b c^4+1044 c^5)
+2 a^4 (b-c)^2 (213 b^4+1073 b^3 c+1680 b^2 c^2+1073 b c^3+213 c^4)
+a^3 (b-c)^2 (114 b^5-365 b^4 c-1549 b^3 c^2-1549 b^2 c^3-365 b c^4+114 c^5)
-2 a^2 (b-c)^4 (63 b^4+286 b^3 c+490 b^2 c^2+286 b c^3+63 c^4)
+5 a (b-c)^4 (b^5+24 b^4 c+83 b^3 c^2+83 b^2 c^3+24 b c^4+c^5)
+2 (b-c)^6 (5 b^4+25 b^3 c+48 b^2 c^2+25 b c^3+5 c^4)) : ... : ....
W lies on the line: {3321,5542}
(6 - 9 - 13) - search numbers: 1.38295593266353, 1.43223206506214, 2.01083185255819
3. The NPCs of IDA', IDB', IDC' are coaxial, the 2nd, other than midpoint of ID, intersection is X(11570) = X(265)-of-intouch-triangle.
Angel Montesdeoca
3. The NPCs of IDA', IDB', IDC' are coaxial, the 2nd, other than midpoint of ID, intersection is X(11570) = X(265)-of-intouch-triangle.
Angel Montesdeoca
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