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Midpoints - Locus

(7)
[APH]: Variation by Leo Giugiuc: Let ABC be a triangle and O,H the circumcenter, orthocenter, resp. Denote: Oa = the reflection of O in HA Ha = the reflection
Antreas Hatzipolakis
7
posts
4:22 AM

Midpoints -- Centroid

(3)
[APH]: Let ABC be a triangle and A'B'C' the pedal triangle of O (medial triangle). Denote: Aa = the reflection of A in OA' A1 = the reflection of A' in OA
Antreas Hatzipolakis
3
posts
Jun 1

A Circle -- Locus

(8)
[APH] ... [CL] M1M2M3 is always perspective with the medial triangle A’B’C’ of ABC. [...] ******************* Are the parallels trough A,B,C to A'M1,
Antreas Hatzipolakis
8
posts
May 25

N -- Locus

(4)
Dear Chris, I am wondering how could we use the property quoted below in qudrangles. Let ABCD be a quadrangle Denote: Na, Nb, Nc, Nd = the NPC centers of BCD,
Antreas Hatzipolakis
4
posts
May 19

A cyclology

(5)
[APH] The configuration with Q = H and P = N is interesting not only for cyclology! Let ABC be a triangle. Denote: P1, P2, P3 = the reflections of N in
Antreas Hatzipolakis
5
posts
May 17

locus

(14)
From: César Lozada [APH] Generalization: Let ABC be a triangle and Q, Q* two isogonal conjugate points and P a variable point. Which is the locus of P such
Antreas Hatzipolakis
14
posts
Apr 30

G,I

(4)
Let ABC be a triangle and P a point. The AP line intersects the circle with diameter BC at A' on the negative side of BC (ie not on the side the vertex A is).
Antreas Hatzipolakis
4
posts
Apr 23

A NPC center on the OI line ?

(4)
... circumcenter of triangles BPC,CPA,APB. >Let A',B',C' be midpoints of AOa,BOb,COc then NPC center of A'B'C' lies on Euler line of ABC. Denote Np = the NPC
Antreas Hatzipolakis
4
posts
Apr 20

I -- Concurrent Circumcircles

(4)
Let ABC be a triangle and I1,I2,I3 the reflections of I in BC,CA,AB, resp. Denote: I12, I13 = the orthogonal projections of I1 on AC,AB, resp. I23, I21 = the
Antreas Hatzipolakis
4
posts
Apr 19

Antipedal triangle -- Loci

(3)
Let ABC be a triangle, P a point and PaPbPc the antipedal triangle of P. Denote: AaAbAc, BaBbBc, CaCbCc = the pedal triangles of Pa, Pb, Pc, resp. A'B'C.' =
Antreas Hatzipolakis
3
posts
Apr 19

Orthologic triangles - Locus

(14)
Orthologic centers and homography Angel Montesdeoca, Centros ortológicos y homografía ...
Antreas Hatzipolakis
14
posts
Apr 15

Cyclologic triangles (Re: Orthologic triangles - Locus)

(5)
[A variation of a configuration by APH] Let ABC be a triangle, A'B'C' a variable triangle w/r to ABC and A1B1C1, A2B2C2 the medial triangles of ABC, A'B'C',
Antreas Hatzipolakis
5
posts
Apr 13
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