HYACINTHOS 26292

[APH]:

Let ABC be a triangle.

Denote:

A'B'C', A"B"C" the cevian triangles of G, I, resp.

Which point is the radical center of the circumcircles of AA'A", BB'B", CC'C" ?

Antreas P. Hatzipolakis

 

 

[Peter Moses]:

Hi Antreas,

X(3216):
on lines {{1,2},{3,1724},{4,5400},{6,47 4},{9,4261},{21,4256},{35,238} ,{36,5247},{38,3678},{39,2238} ,{44,3916},{46,2390},{56,4551} ,{58,404},{65,1739},{72,3670}, {73,3911},{100,595},...}.
midpoint of X(1201) and X(3214).
reflection of X(1) in X(1201).
{X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1,43,3293),(1,6048,3679),(2,3 86,1),(2,9534,10479),(3,4383,1 724),(8,995,1),(10,1193,1),(42 ,1125,1),(43,978,1),(72,3752,3 670),(614,3811,1),(899,1193,10 ),(936,2999,1),(975,5256,1),(1 149,3244,1),(1698,5313,1),(362 4,5312,1),(9534,10479,3679),.. .

on the Feuerbach of the tangential triangle.
X(i)-aleph conjugate of X(j) for these (i,j): {{1, 191}, {6, 1045}, {21, 20}, {28, 1714}, {58, 3216}, {81, 2}, {100, 4427}, {174, 1762}, {259, 2938}, {266, 1046}, {365, 846}, {366, 1761}, {509, 1781}, {662, 3882}, {6727, 3}}.
X(3699)-beth conjugate of X(3216).
X(741)-he conjugate of X(6).
X(i)-zayin conjugate of X(j) for these (i,j): {{56, 1724}, {58, 3216}, {667, 4040}, {1193, 1}, {1203, 3293}, {2260, 1743}, {2308, 43}, {2309, 87}, {3122, 9359}, {3733, 3737}, {4057, 513}, {10457, 58}}.
X(i)-Ceva conjugate of X(j) for these (i,j): {{58, 1}, {404, 3}}.
X(3159)-cross conjugate of X(1).
crosspoint of X(662) and X(7035).
crossdifference of every pair of points on line (649, 3726)
crosssum of X(i) and X(j) for these (i,j): {{513, 8054}, {661, 3248}}.
barycentric product X(81)X(3159).
barycentric quotient X(3159)/X(321).

Best regards,

Peter.