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Re: Radical axes, Euler lines, Circumcircle

(4)
GENERALIZATION: Let ABC be a triangle. Denote: R1, R2, R3 = three arbitrary lines passing through H. Aa, Ab, Ac = the orthogonal projections of A on R1, R2,
Antreas Hatzipolakis
4
posts
5:18 AM

H, NPC, Orthologic

(3)
[APH]: Let ABC be a triangle, A'B'C' the pedal triangle of H. Denote: Na, Nb, Nc = the reflections of N in HA', HB', HC', resp. N1, N2, N3 = the NPC centers of
Antreas Hatzipolakis
3
posts
Apr 28

A Circumcenter on the OI line

(3)
[‎Tran Quang Hung‎]: Let ABC be a triangle with incircle (I). Circle (wa) passes through B,C and is tangent to (I). Similarly, we have circle (wb),(wc).
Antreas Hatzipolakis
3
posts
Apr 27

H, Radical axes

(5)
[APH]: Let ABC be a triangle and A1B1C1 the pedal triangle of H. Denote: A;, B', C' = the reflections of G in BC, CA, AB, resp. (Oa), (Ob), (Oc) = the circles
Antreas Hatzipolakis
5
posts
Apr 27

N, concurrent Euler lines

(7)
[APH] (Hyacinthos #25843 rephrased): Let ABC be a triangle and A1B1C1 the
Antreas Hatzipolakis
7
posts
Apr 25

Reflection point of a line wrt triangle ABC.

(6)
Definition: Let ABC be a triangle and L a line. Denote: La, Lb, Lc = the reflections of L in BC, CA, AB, resp. A*B*C* = the triangle bounded by La, Lb, Lc. It
Antreas Hatzipolakis
6
posts
Apr 24

Euler line, Orthologic

(3)
CONJECTURE: Let ABC be a triangle, P a point on the Euler line and A'B'C' the pedal triangle of P. Let Pab, Pac, Pbc, Pba, Pca, Pcb be same points on the Euler
Antreas Hatzipolakis
3
posts
Apr 23

Re: Orthocenter lies on Euler line

(7)
[Tran Quang Hung] Let ABC be a triangle with NPC center N. A',B',C' are reflections of N in the perpendicular bisectors of BC,CA,AB, reps. Na,Nb,Nc are NPC
Antreas Hatzipolakis
7
posts
Apr 22

I, pedal, NPCs

(3)
[APH]: Let ABC be a triangle and A'B'C' the pedal triangle of I. Denote: T1, T2, T3 = the pedal triangles of A, B, C wrt triangle A'B'C'. Na, Nb, Nc = the NPC
Antreas Hatzipolakis
3
posts
Apr 22

Feuerbach

(22)
[APH]: Another construction of the Feuerbach point: Let ABC be a triangle and A'B'C' the pedal triangle of I. Denote: T = the excentral triangle of A'B'C' T1,
Antreas Hatzipolakis
22
posts
Apr 22

O, NPC, Euler lines, parallelogic

(7)
[APH]: Let ABC be a triangle and A'B'C' the pedal triangle of O. Denote: Aa, Ab, Ac = the orthogonal projections of A' on OA, OB, OC, resp. Ba, Bb, Bc = the
Antreas Hatzipolakis
7
posts
Apr 22

O, H, midpoints, NPCs

(5)
[Antreas Hatzipolakis]: https://beta.groups.yahoo.com/neo/groups/Hyacinthos/conversations/messages/25768 Let ABC be a triangle and HaHbHc, NaNbNc the pedal
Antreas Hatzipolakis
5
posts
Apr 20

Homothetic

(7)
Let ABC a triangle and P a point . Denote: Na, Nb, Nc = the NPC centers of PBC, PCA, PAB, resp. D = the orthologic center (NaNbNc, ABC) Oa, Ob, Oc = the
Antreas Hatzipolakis
7
posts
Apr 18

Concurrent circles, locus

(6)
Variation of Hyacinthos 25709 Let ABC be a triangle, P a point and A'B'C'
Antreas Hatzipolakis
6
posts
Apr 17

A Property of N

(5)
Let ABC be a triangle and A'B'C' the pedal triangle of N. Denote Na, Nb, Nc = the NPC centers of NB'C', NC'A', NA'B', resp. A", B", C" = the reflections of
Antreas Hatzipolakis
5
posts
Apr 17
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