1861. A Locus For K001-Neuberg Cubic (Part 2)

1860. A Locus For K001-Neuberg Cubic of ABC

1859. Collinear Points On the Radical Axes

1858. A Construction For X(1319)-Bevan-Schröder Point

1857. Isogonal Curves and Isogonal Perspectors

 1.) Let P be a point and A1B1C1 cevian triangle of P.

A2: inverse of A1 in the circle PBC. Define B2, C2 cyclically.
*ABC and A2B2C2 are perspective if P lies on a curve C passing through X(2)-centroid, X(4)-Orthocenter and X(13)-1st Fermat-Toricelli point.
For X(2)-centroid, X(4)-Orthocenter and X(13)-1st Fermat-Toricelli point perspectors of ABC and A2B2C2 are X(524), X(403) and X(36211).

2.) Let P be a point and A1B1C1 circumcevian triangle of P.
A2: inverse of A1 in the circle PBC. Define B2, C2 cyclically.
**ABC and A2B2C2 are perspective if P lies on a curve C*  passing through X(6)-symmedian point, X(3)-Circumcenter and X(15)-1st Isodynamic point.
For  X(6)-symmedian point, X(3)-Circumcenter and X(15)-1st Isodynamic point perspectors of ABC and A2B2C2 are X(111), X(5504) and X(36209).

*** Do curves C and C* defined in problem 1 and 2 are isogonal conjugates?
**** Interestingly perspectors in problem 1 and perspectors in problem 2 are isogonal conjugate points. 
Does this property valid for all perspectors?

1856. A Construction For Barycentric Cube Of Nagel's Point

1855. A Symmedian Point On Euler Line

1854. Myakishev Associate Triangles

1853. A Construction For X(5497) = 5th HATZIPOLAKIS-MONTESDEOCA POINT

 Let I=X(1) incenter of ABC. Circle BIC ıntersects the AC and AB at Ab, Ac. Define Ba,Bc, Ca,Cb cyclically.

Inversion of the line BC in the circle (IBcCb) is a cirlcle GammaA. Define GammB, GammaC cyclically.

*  GammaA, GammB, GammaC are concurrent circles. Concurrency point is X(5497) =  5th HATZIPOLAKIS-MONTESDEOCA POINT.

1852. Points On Circumcircle

1851. Points On Euler Line

1850. Points On the Line X(1)X(3)

1849. Collinear Points

1848. Concurrent Circles

1847. General Case Of Problem 1833

1846. A Circle Center on Euler Line

1845. Circle Passing Through Isogonal Conjugate

1844. Inscribed Triangles

1843. A Locus For K018-Brocard (second) cubic

1842. Collinear Points

1841. Efthimis Circle

1840. Inversion of Inversion

1839. Perspective Triangles

1838. Another Myakishev Associate Triangles By Inversion