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### O, H, Reflections

(4)

[APH]: Let ABC be a triangle. The reflections of HA in OA, OB, OC bound a triangle Ta The reflections of HB in OA, OB, OC bound a triangle Tb The reflections
Antreas Hatzipolakis

Jul 20

### Na, Concurrent Euler lines

(3)

[Tran Quang Hung] = buratinogigle (*) Let ABC be a triangle, A'B'C' the pedal triangle of I and A"B"C" the cevian triangle of the Nagel point Na. The Euler
Antreas Hatzipolakis

Jul 19

### A NPC through O, an orthocenter on the circumcircle

(3)

[Le Viet An]: Dear Mr Rodinos Let ABC be a triangle and L the Euler line. Denote: E = the point of concurrence of the reflections of L in BC, CA, AB, resp. [
Antreas Hatzipolakis

Jul 16

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### Concurrent Euler lines

(13)

[APH]: Let ABC be a triangle. Denote: Ab,Ac = the orthogonal projections of A on IB, IC, resp. La = the Euler line of AAbAc Laa, Lab, Lac = the reflections of
Antreas Hatzipolakis

Jul 15

### A NPC touches the circumcircle

(4)

[Le Viet An] (*): Let ABC be a triangle and L a line passing through O. Denote: A',B',C' = the orthogonal projections of A,B,C on L, resp. La, Lb, Lc = the
Antreas Hatzipolakis

Jul 15

### Points on the circumcircle

(4)

[Le Viet An]: Let ABC be a triangle, L a line through O and P a point on the circumcircle (O) of ABC Denote: A1, B1, C1 = the intersections of the lines PA,
Antreas Hatzipolakis

Jul 13

### Point on the NPC

(5)

[APH]: Let ABC be a triangle and P a point. Denote: Ab, Ac = the orthogonal projections of A on PB, PC, resp. Similarly Bc, Ba and Ca, Cb. La, Lb, Lc = the
Antreas Hatzipolakis

Jul 13

### Reflection triangle, radical axes

(3)

[APH]: Let ABC be a triangle and A'B'C' the reflection triangle (ie A', B', C' = the reflections of A, B, C in BC, CA, AB, resp) Denote: (Oa), (Ob), (Oc) = the
Antreas Hatzipolakis

Jul 11

### Poncelet, a circle

(3)

[APH]: Let ABC be a triangle and P a point. Denote: P* = the Poncelet point of (ABCP) (ie the point the NPCs of ABC, PBC, PCA, PAB concur at) A*, B*, C* = the
Antreas Hatzipolakis

Jul 10

### H, I, Feuerbach, a circle

(3)

[Le Viet An]: Let ABC be a triangle and DaDbDc the pedal triangle of H. Denote: Ab, Ac = the orthogonal projections of A on IB, IC, resp. F, Fa, Fb, Fc = the
Antreas Hatzipolakis

Jul 9

### X110, locus

(6)

[APH]: Let ABC be a triangle, P a point and A'B'C' the pedal triangle of P. Denote: Ea = the X110 of AB'C' (ie the point the reflections of the Euler line of
Antreas Hatzipolakis

Jul 4

### Concurrent Euler Lines

(19)

[APH]: Dear Mr rodinos (*), I have two new problems (and synthetic proofs): *Probelm 1*. Let Ia, Ib, Ic be A, B, C-excenters of a triangle ABC, resp. Let Ka,
Antreas Hatzipolakis

Jul 4

### Simson lines, locus

(5)

Let ABCD be a quadrangle. Denote: S = the Poncelet point of (ABCD) (ie the point the NPCs of BCD, CDA, DAB, ABC concur at) Ma, Mb, Mc, Md = the medial
Antreas Hatzipolakis

Jul 1

### Isogonal conjugate of Perspector lies on Euler line

(4)

[APH]: 1. Let ABC be a triangle and P a point. Denote: Pa, Pb, Pc = the reflections of P in BC, CA, AB, resp. D = AO /\ PbPc E = BO /\ PcPa F = CO /\ PaPb
Antreas Hatzipolakis

Jul 1

### O, Homothetic

(4)

[APH]: Let ABC be a triangle and A'B'C' the pedal triangle of a point P. Denote: Bc, Cb = the orthogonal projections of B', C' on AB, AC, resp. B3, C2 = the
Antreas Hatzipolakis

Jun 29

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## Trending Topics

See All- O, H, Reflections 4 Posts
- Na, Concurrent Euler lines 3 Posts
- A NPC through O, an orthocenter... 3 Posts
- Concurrent Euler lines 13 Posts
- A NPC touches the circumcircle 4 Posts

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