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### Re: Radical axes, Euler lines, Circumcircle

(3)

[APH]: Let ABC be a triangle, P a point and A'B'C' the cevian triangle of P. Denote: (Oa), (Ob), (Oc) = the circles with diameters AA', BB', CC', resp (O1),
Antreas Hatzipolakis

10:08 PM

### 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

3:56 AM

### 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

Apr 27

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### 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

Apr 27

### N, concurrent Euler lines

(7)

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

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

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

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

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

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

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

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

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

Apr 18

### Concurrent circles, locus

(6)

Variation of Hyacinthos 25709 Let ABC be a triangle, P a point and A'B'C'
Antreas Hatzipolakis

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

Apr 17

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## Trending Topics

See All- Re: Radical axes, Euler lines,... 3 Posts
- H, NPC, Orthologic 3 Posts
- A Circumcenter on the OI line 3 Posts
- H, Radical axes 5 Posts
- N, concurrent Euler lines 7 Posts

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