HYACINTHOS 26107

[Tran Quang Hung‎]:

 

Let ABC be a triangle.

Denote:

D, E, F = the points of contact of the circumcircle and the A-, B-, C- mixtilinear incircles, resp.

XYZ = the antipedal triangle of I wrt triangle DEF.

DEF, XYZ are perspective.

The perspector lies on the OI line.

[Peter Moses]:

Hi Antreas,

 

a (5 a-b-c) (a+b-c) (a-b+c):: 

on lines {{1,3},{2,4315},{7,551}, {9,11194},{10,4308},{101,604}, {104,3062},{106,269},...}.

isogonal conjugate of X(4900).

X(21)-beth conjugate of X(165).

{X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1,36,165),(1,46,11531),(1,56, 3361),(1,165,9819),(1,2093, 11224),(1,3361,3339),(3,56, 13370),(56,1319,57),(56,1420, 1),(56,1617,36),(57,1319,1),( 57,1420,1319),(354,13384,1),( 999,3576,1),(999,5126,3576),( 1385,3333,1),(1388,3340,1),( 1470,2078,5010),(3304,3601,1), (4308,5265,10),(10246,11529,1) .

(4 R-r) X[1] - 4 r X[3].

isoconjugate of X(j) and X(j) for these (i,j): {{1, 4900}, {522, 6014}}.

crosssum of X(i) and X(j) for these (i,j): {{2170, 4814}}.

barycentric product X(i)X(j) for these {i,j}: {{57, 3241}, {651, 6006}, {1014, 4029}, {4554, 8656}}.

barycentric quotient X(i)/X(j) for these {i,j}: {{6, 4900}, {1415, 6014}, {3241, 312}, {4029, 3701}, {4982, 3702}, {6006, 4391}, {8656, 650}}.

Searches: {0. 067342968504264269124272376682 5,0. 350183436222174199446216358749 ,3. 36714842521321345621361883413} .

 

 

Best regards,

Peter Moses.