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A locus problem

(17)
[APH]: Let ABC be a triangle, A'B'C' the cevian triangle of G and P a point. Denote: Ma, Mb, Mc = the midpoints of AP, BP, CP, resp. A" = PG /\ B'C', B" = PG
Antreas Hatzipolakis
17
posts
Jun 21

Reflections, NPCs, perspective, orthologic

(3)
[APH]: Let ABC be a triangle and P a point. Denote: A', B', C' = the reflections of A, B, C in P, resp. Ab, Ac = the orthogonal projections of A' on BP, CP,
Antreas Hatzipolakis
3
posts
Jun 19

Circumparallelogic triangles

(3)
Dear C├ęsar Additional information to your extensive lists of circumorthologic triangles and circumparallelogic triangles. If the triangles A1B1C1 and A2B2C2
Antreas Hatzipolakis
3
posts
Jun 17

Circumorthologic Triangles

(5)
[Angel Montesdeoca]: Another example of circumorthologic triangles Let A'B'C' be the orthic triangle. Let La be the antiorthic axis of AB'C', and define Lb, Lc
Antreas Hatzipolakis
5
posts
Jun 17

H, Orthologic

(11)
[APH]: Let ABC be a triangle and A'B'C' the pedal triangle of H. Denote: A", B", C" = the reflections of A', B', C' in A, B, C, resp. N1, N2, N3 = the NPC
Antreas Hatzipolakis
11
posts
Jun 15

A circumcenter on the Euler line

(11)
[APH]: Let ABC be a triangle. Denote: N1, N2, N3 = the NPC centers of OBC, OCA, OAB, resp. Na, Nb, Nc = the reflections of N1, N2, N3 in AO, BO, CO, resp. The
Antreas Hatzipolakis
11
posts
Jun 14

Re: H, Parallelogic, orthologic

(7)
[APH]: Let ABC be a triangle and A'B'C' the pedal triangle of H. Denote: N1 = the NPC center of AB'C' Na = the reflection of N1 in HA'. Similarly Nb, Nc. 1.
Antreas Hatzipolakis
7
posts
Jun 13

G, radical center

(4)
[APH]: Let ABC be a triangle and A'B'C' the cevian triangle of G. Denote: (Oa) = the reflection of the circle with diameter AA' in BC. (Ob) = the reflection of
Antreas Hatzipolakis
4
posts
Jun 12

A Lester - like circle

(3)
[Alexander Skutin (solver6)] (*) Let F1. F2 be the first and second Fermat points of ABC and A'B'C' the cevian triangle of F1. The circumcenter and the
Antreas Hatzipolakis
3
posts
Jun 11

Radical center, Euler line, locus

(3)
Variation of Hyacinthos #26145 ... Let ABC be a triangle, P a point and
Antreas Hatzipolakis
3
posts
Jun 11

Orthologic

(24)
[APH]: Let ABC be a triangle and A'B'C' the pedal triangle of O. Denote: Ab, Ac = the reflections of B', C' in AO, resp. Na = the NPC center of OAbAc.
Antreas Hatzipolakis
24
posts
Jun 10

N, Concyclic

(10)
[Le Viet An]: Let ABC be a triangle and MaMbMc the pedal triangle of O. Denote: Pa = AO /\ MbMc, Pb = BO /\ McMa, Pc = CO /\ MaMb N, Na, Nb, Nc = the NPC
Antreas Hatzipolakis
10
posts
Jun 8

Isogonal conjugates, centroid

(3)
[APH]: Generalization of Romantics of Geometry Problem 816
Antreas Hatzipolakis
3
posts
Jun 2

N, H, Euler lines, parallelogic

(3)
[APH]: Let ABC be a triangle and A'B'C' the pedal triangle of N. Denote: Ab, Ac = the orthogonal projections of A' on BH, CH, resp. La = the Euler line of
Antreas Hatzipolakis
3
posts
May 31

Radical axes, locus

(9)
[ Antreas Hatzipolakis]: Let ABC be a triangle, P a point and A'B'C' the antipedal triangle of P. Denote: Ab, Ac = the orthogonal projections of A on PB, PC,
Antreas Hatzipolakis
9
posts
May 17
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