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I, Concurrent Euler lines

(7)
[Le Viet An]: Let ABC be a triangle and IaIbIc the antipedal triangle of I. Let L be a line passing through I. Denote: A', B', C' = the orthogonal projections
Antreas Hatzipolakis
7
posts
Jul 21

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
4
posts
Jul 20

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
3
posts
Jul 16

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
13
posts
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
4
posts
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
4
posts
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
5
posts
Jul 13

Feuerbach points, a NPC

(3)
[Le Viet An]: Let ABC be a triangle and Fe, Fa, Fb, Fc the Feuerbach points. Denote: PaPbPc = the pedal triangle of I. Qa, Qb, Qc = the orthogonal projections
Antreas Hatzipolakis
3
posts
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
3
posts
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
3
posts
Jul 10

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
6
posts
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
19
posts
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
5
posts
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
4
posts
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
4
posts
Jun 29
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