X3632

H⁻¹(X8; M, 1/2)

X3632 = homothetic center of outer Garcia triangle and mid-triangle of medial and anticomplementary triangles
< 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) { 1, 2 }: Nagel Line { 40, 550 }: Central Line L(40, 550) { 35, 956 }: Central Line L(35, 956) { 69, 1266 }: Central Line L(69, 1266) { 72, 3586 }: Central Line L(72, 3586) { 80, 3680 }: Central Line L(80, 3680) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1 = INCENTER (0.5714, 0.2333) X_2 = CENTROID (0.5374, 0.2000) X_40 = BEVAN POINT (0.4286, -0.0292) X_550 = MIDPOINT OF X(3) AND X(20) (0.4439, -0.0448) X_35 = {X(1),X(3)}-HARMONIC CONJUGATE OF X(36) (0.5373, 0.1706) X_956 = INTERSECTION OF LINES X(1)X(6) AND X(3)X(8) (0.4790, 0.1235) X_69 = SYMMEDIAN POINT OF THE ANTICOMPLEMENTARY TRIANGLE (0.4122, 0.0654) X_1266 = ISOTOMIC CONJUGATE OF X(1120) (2.8367, 1.7996) X_72 = ISOGONAL CONJUGATE OF X(28) (0.4367, 0.0733) X_3586 = INTERSECTION OF LINES X(1)X(4) AND X(30)X(57) (0.5472, 0.1370) X_80 = REFLECTION OF INCENTER IN FEUERBACH POINT (0.8980, -0.1000) X_3680 = com(EXTOUCH TRIANGLE) (0.2679, 0.0583) X_3632 = H-1(X(8); M, 1/2) (0.3673, 0.0333) A B C X1 X2 X40 X550 X35 X956 X69 X1266 X72 X3586 X80 X3680 X3632 (a, b, c) = (5, 6, 7) | AB = 1

X3632 (H⁻¹(X8; M, 1/2)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(bc(3a - 2b - 2c) : ca(3b - 2c - 2a) : ab(3c - 2a - 2b)\)
Barycentrics: \(3a - 2b - 2c : 3b - 2c - 2a : 3c - 2a - 2b\)
Search Value (6, 9, 13): \(7.324670207647\)
▸ Alternate Coordinates1 form

  • Trilinears: \(5 r - 4 R \sin B \sin C : :\)

▸ Linear Combinations1 combination
▸ Incident Central Lines25 lines

{1, 2}, {3, 5288}, {4, 4900}, {5, 16200}, {6, 4007}, {9, 3943}, {35, 956}, {36, 5687}, {37, 4034}, {40, 550}, {44, 4873}, {45, 4727}, {46, 6762}, {55, 5258}, {56, 17573}, {57, 10944}, {58, 4720}, {63, 11010}, {65, 3894}, {69, 1266}, {72, 3586}, {75, 4888}, {80, 3680}, {90, 12641}, {100, 7280}

▸ Functional Relations2 relations

  • X3632 = {X8,X10}-harmonic conjugate of X4668

  • X3632 = homothetic center of outer Garcia triangle and mid-triangle of medial and anticomplementary triangles