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Concurrent NPCs

(18)
[APH]: Let ABC be a triangle and A'B'C' the pedal triangle of I. Denote: A" = AH /\ B'C' B" = BH /\ C'A' C" = CH /\ A'B' The NPCs of A"HI, B"HI, C"HI are
Antreas Hatzipolakis
18
posts
5:16 AM

A Line

(3)
[APH]: Let ABC be a triangle, P a point and MaMbMc, PaPbPc the pedal triangles of O, P, resp. Deonte: M1, M2, M3 = the midpoints of AP, BP, CP, resp. The
Antreas Hatzipolakis
3
posts
Jan 15

Symmetric points on the sides of triangle

(6)
NOTE: I change the notation of Antreas H. and Kadir Altintas Let ABC be a triangle. 0. GENERAL CASE The circle B(ra) of center B and radius ra, cut BC into
Antreas Hatzipolakis
6
posts
Jan 14

Locus problem

(15)
Let ABC be a triangle, P a point and A'B'C' the cevian triangle of P. Denote: A" = the other than P intersection of the circles (B', B'P) and (C', C'P) B" =
Antreas Hatzipolakis
15
posts
Jan 13

H, perspective

(14)
[APH]: Let ABC be a triangle and A'B'C' the cevian triangle of Η. Denote: Ab, Ac = the orthogonal projections of A' on BB', CC', resp. A2, A3 = the orthogonal
Antreas Hatzipolakis
14
posts
Jan 13

H, NPC, Parallelogic

(3)
Let ABC be a triangle and A'B'C' the cevian triangle of H. Denote: MaMbMc = the midheight triangle. (ie Ma, Mb, Mc = the midpoints of AA', BB', CC', resp.) Ab,
Antreas Hatzipolakis
3
posts
Jan 10

N, H, O , NPC, Euler lines.

(3)
[APH]: Let ABC be a triangle. Denote: Nah, Nao = the orthogonal projections of N on AH, AO, resp. La = the Euler line of ANahNao. Similarly Lb, Lc. N1 = the
Antreas Hatzipolakis
3
posts
Jan 9

Circumcevian, Concurrent Euler lines

(7)
Thanks, Peter, for your reply !! (Hyacinthos 27017 ) The general problem is: Let
Antreas Hatzipolakis
7
posts
Jan 5

O, Euler lines, parallelogic

(4)
[APH]: Let ABC be a triangle. Denote: Oa, Ob, Oc = the reflections of O in BC, CA, AB, resp. Oab, Oac = the reflections of Oa in AB, AC, resp. Obc, Oba = the
Antreas Hatzipolakis
4
posts
Jan 3

H, Orthologic

(17)
[APH]: Let ABC be a triangle and A'B'C' the cevian triangle of H. Denote: A"B"C" = the midheight triangle (ie A", B", C" = the midpoints of AA', BB', CC',
Antreas Hatzipolakis
17
posts
Dec 30, 2017

A circumcenter on the Euler line

(22)
GENERALIZATION Let ABC be a triangle and Ra, Rb, Rc three lines perpendicular to BC, CA, AB, resp. Let A*B*C* be the triangle bounded by Ra, Rb, Rc The Euler
Antreas Hatzipolakis
22
posts
Dec 28, 2017

Pedal, Euler lines

(4)
[APH]: Let ABC be a triangle, P a point and A'B'C' the pedal triangle of P. Denote: La, Lb, Lc = the Euler lines of AB'C', BC'A', CA'B', resp. Oa, Ob, Oc = the
Antreas Hatzipolakis
4
posts
Dec 26, 2017

A peprspector and an orthologic center on the Euler line

(6)
[APH]: CONJECTURE Let ABC be a triangle, (M) a circle and P a point. Denote: (Oa), (Ob), (Oc) = the circumcircles of MBC, MCA, MAB, resp. (O1), (O2), (O3) =
Antreas Hatzipolakis
6
posts
Dec 20, 2017

I, Coaxial

(13)
[APH]: Let ABC be a triangle and A'B'C' the pedal triangle of I. Denote: A", B", C" = the antipodes of A', B', C', resp. in the incircle. Na, Nb, Nc = the NPC
Antreas Hatzipolakis
13
posts
Dec 10, 2017

Midway

(7)
Let ABC be a triangle and P a point. Denote: Oa, Ob, Oc = the corcumcenters of PBC, PCA, PAB, resp. OaaOabOac = the midway triangle of Oa (ie Oaa, Oab, Oac =
Antreas Hatzipolakis
7
posts
Nov 19, 2017
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