# Topics List

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Reflections - Loci
(3)
1. La, Lb, Lc are concurrent? (the entire plane, with point of concurrence the isogonal conjugate of P) Confirmed 2. ABC, A'B'C' are perspective? (the entire

Antreas Hatzipolakis

Feb 26

# Topics List

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Re: Point on the IH line
(4)
[APH]: The perpendiculars to HIa, HIb, HIc from A,B,C, resp. bound triangle A"B"C". Which point is the circumenter of A"B"C" ? Is it lying on the IH line? ...

Antreas Hatzipolakis

Feb 24

# Topics List

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Collinear Points
(10)
... *********************************************** [César Lozada] It is X(1141). [Peter Moses] Hi Antreas, X(1141). Best regards Peter. [APH]: [APH]: Let ABC

Antreas Hatzipolakis

Feb 19

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# Topics List

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Interesting circle
(4)
... Extraversions: Following are "theoretic" ie written without drawings. Hope they are true..... :-) We have two incircles in the configuration, so there

Antreas Hatzipolakis

Feb 11

# Topics List

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Cyclology of hexagon
(6)
From: Angel Montesdeoca [Attachment(s) <#14b5bc8ac33fefb1_TopText> from Angel Montesdeoca included below] Let's rewrite the Anopolis #2404 and Anopolis #2406

Antreas Hatzipolakis

Feb 5

# Topics List

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A property of X(597) and a locus
(6)
Dear Seiichi, The Eulerline through the centroids of quadrangles made from 4 centroids, 4 circumcenters, and 4 orthocenters of its component triangles is the

Antreas Hatzipolakis

Jan 29

# Topics List

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Reflections - NPCs - Cyclologic triangles
(4)
... Discussion here: https://www.facebook.com/photo.php?fbid=773944689348296&set=a.237986886277415.57448.100001983178784&type=1&theater APH

Antreas Hatzipolakis

Jan 28

# Topics List

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H - Concurrent NPCs (Re: NPC - Orthologic triangles)
(5)
[APH] Are lying the 6 NPC centers N1 N2, N3, N_A, N_B, N_C on a conic (Circle?) ? They are concyclic on the circle with radius OH/2 and center X(6102)=19th

Antreas Hatzipolakis

Jan 25

# Topics List

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Mapping of P on the pedal circle of P
(4)
[APH] 1. The circumcenter of IaIbIc is the isogonal cojugate of P. 2. The parallels through A', B', C' of the perpendicular bisectors of IbIc, IcIa, IaIb,

Antreas Hatzipolakis

Jan 21

# Topics List

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Euler Line
(12)
From: César Lozada [APH] For which (m,n) the perspector lies on the Euler line? For all m,n. The perspector Z(m,n) has trilinears: Z(m,n) =

Antreas Hatzipolakis

Jan 20

# Topics List

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A Miquel point
(4)
... Dear César and Randy Thanks !! Generalization. Let ABC be a triangle and A'B'C' the cevian triangle of a point P. The parallel to BC through the midpoint

Antreas Hatzipolakis

Jan 16

# Topics List

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A Circumcenter
(3)
... Synthetic proof by Telv Cohl http://www.artofproblemsolving.com/Forum/viewtopic.php?f=47&t=620608&p=3708849#p3708849 We have now a locus problem: Let Q, Q'

Antreas Hatzipolakis

Jan 11

# Topics List

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Collinear N's
(4)
Antreas Hatzipolakis: Let ABC be a triangle and N, Nn, Nh the NPC centers ... [Peter Moses]: Nn is on lines {{5,51},{195,5640},{5943,6153}} Midpoint X(143) &

Antreas Hatzipolakis

Jan 8

# Topics List

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Orthologic triangles - Locus
(10)
From: César Lozada 5. OaObOc, O1O2O3 are orthologic? [César Lozada]: 5) Couln´t calculate ************************ I think H lies on the locus

Antreas Hatzipolakis

Jan 7

# Topics List

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Pedal Triangle - Orthocenters - Collinear points
(8)
[APH] Equivalently: Let ABC be a triangle and P a point. Denote: Aa = (Parallel through B to PC) /\ (Parallel through C to PB) A1 = the isogonal conjugate of

Antreas Hatzipolakis

Jan 3

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