X3626

H⁻¹(X1; M, -2)

X3626 = midpoint of X8 and X10
< A B C >: Reference Triangle △ABC [ A B ]: Sideline AB (Base c = 1) [ B C ]: Sideline BC (Side a) [ C A ]: Sideline CA (Side b) { 8, 10 }: Nagel Line { 1, 2 }: Nagel Line { 44, 594 }: Central Line L(44, 594) { 355, 382 }: Central Line L(355, 382) { 517, 546 }: Central Line L(517, 546) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_8 = NAGEL POINT (0.4694, 0.1333) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_1 = INCENTER (0.5714, 0.2333) X_2 = CENTROID (0.5374, 0.2000) X_44 = -LINE CONJUGATE OF X(1) (2.1429, 2.0996) X_594 = ISOGONAL CONJUGATE OF X(593) (0.5025, 0.1672) X_355 = FUHRMANN CENTER (0.5408, 0.2645) X_382 = REFLECTION OF CIRCUMCENTER IN ORTHOCENTER (0.7245, 0.6894) X_517 = ISOGONAL CONJUGATE OF X(104) (0.8180, 0.7154) X_546 = MIDPOINT OF X(4) AND X(5) (0.5842, 0.3223) X_3626 = H-1(X(1); M, -2) (0.4949, 0.1583) A B C X8 X10 X1 X2 X44 X594 X355 X382 X517 X546 X3626 (a, b, c) = (5, 6, 7) | AB = 1

X3626 (H⁻¹(X1; M, -2)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(bc(2a - 3b - 3c) : :\)
Barycentrics: \(2a - 3b - 3c : 2b - 3c - 3a : 2c - 3a - 3b\)
Search Value (6, 9, 13): \(3.803194146278\)
▸ Alternate Coordinates1 form

  • Trilinears: \(5 r - 6 R \sin B \sin C : :\)

▸ Linear Combinations1 combination
▸ Incident Central Lines10 lines

{1, 2}, {40, 3529}, {44, 594}, {45, 2321}, {106, 1339}, {355, 382}, {515, 550}, {517, 546}, {952, 3530}, {960, 2802}

▸ Functional Relations4 relations

Notes

Let OA be the circle centered at the A-vertex of the 6th mixtilinear triangle and passing through A; define OB, OC cyclically. X3626 is the radical center of OA, OB, OC. (Randy Hutson, August 28, 2020)