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Re: Orthocenter lies on Euler line

(4)
[Tran Quang Hung]: Let ABC be a triangle with circumcenter O. Ka,Kb,Kc are circumcenters of triangles OBC,OCA,OAB. Ka*,Kb*,Kc* are isogonal conjugate of
Antreas Hatzipolakis
4
posts
Mar 24

Concurrent Euler lines locus

(5)
Variation: Let ABC be a triangle and P a point. Denote: A'B'C' = the cevian triangle of P A"B"C" = the circumcevian triangle of P. Ab, Ac = the orthogonal
Antreas Hatzipolakis
5
posts
Mar 22

NPC Coaxial, Loci

(3)
Let ABC be a triangle and P a point. Denote: A', B', C' = the reflections of P in BC, CA, AB, resp. O', H' = the circumcenter, orthocenter of A'B'C', resp. 1.
Antreas Hatzipolakis
3
posts
Mar 18

Circumcenters on the Euler line

(7)
Let ABC be a triangle and A'B'C' the pedal triangle of N. Denote: Ab, Ac = the orthogonal projections of A' on NB', NC', resp. A* = NA' intersection AbAc.
Antreas Hatzipolakis
7
posts
Mar 18

Circumcenter, Locus

(3)
Let ABC be a triangle and P a point. Denote: A', B', C' = the reflections of P in BC, CA, AB, resp. Which is the locus of P such that the circumcenter O' of
Antreas Hatzipolakis
3
posts
Mar 17

Euler lines, Locus

(6)
[APH]: Let ABC be a triangle and P a point. Denote: A', B', C' = the reflections of P in BC, CA, AB, resp. Ab, Ac = intersections of BC and A'B', A'C', resp.
Antreas Hatzipolakis
6
posts
Mar 16

H, O, NPC, Collinear, Envelope

(4)
[Antreas Hatzipolakis]: Let ABC be a triangle, A'B'C' the cevian triangle of H and L a line. Denote: A* = L Intersection AA' B* = L Intersection BB' C* = L
Antreas Hatzipolakis
4
posts
Mar 14

H, Coaxial NPCs

(3)
[APH]: I do not remember if I have posted it before...... Let ABC be a triangle and P a point. Denote: A', B', C' = the reflections of P in BC, CA, AB, resp.
Antreas Hatzipolakis
3
posts
Mar 13

O, Concurrent NPCs

(4)
[APH]: Let ABC be a triangle. Denote; A', B', C' = the reflections of O in BC, CA, AB, resp. [A', B', C' are the reflections of A,B,C in N, resp.] Ab, Ac = the
Antreas Hatzipolakis
4
posts
Mar 11

"Hexagon flower'

(3)
From "Romantics of Geometry" #574 [Tran Quang Hung‎]
Antreas Hatzipolakis
3
posts
Mar 10

H, O, Coaxial

(5)
[APH]: Let ABC be a triangle and H1B1C1 the pedal triangle of H. Denote; A', B', C' = the reflections of O in BC, CA, AB, resp. Ab, Ac = the orthogonal
Antreas Hatzipolakis
5
posts
Mar 10

Points on the Incircle

(8)
[Peter Moses]: Hi Antreas, An intouch version. A’B’C’ = intouch triangle. (Ja) = incircle of AB’C’ circle tangent externally to (Ja) (Jb) & (Jc),
Antreas Hatzipolakis
8
posts
Mar 9

Perspective, locus

(3)
[APH]: Let ABC be a triangle, P a point and A'B'C' the cevian triangle of P. Denote: A* = (Parallel from B' to CC') intersection (Parallel from C' to BB')
Antreas Hatzipolakis
3
posts
Mar 8

Pedal, NPC, radical axes, parallelogic, locus

(5)
[Antreas Hatzipolakis]: Let ABC be a triangle, P, Q two isogonal conjugate points and A'B'C' the pedal triangle of Q. Denote: P, Pa, Pb, Pc = same points of
Antreas Hatzipolakis
5
posts
Mar 3

A conic

(5)
[APH]: Let ABC be a triangle. Denote: La = the perpendicular to AI at I. The perpendicular to AB at B intersects La at A2 The perpendicular to AC at C
Antreas Hatzipolakis
5
posts
Feb 28
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