X2067

POINT CAROLI II

X2067 = homothetic center of 1st Kenmotu diagonals triangle and anti-tangential midarc triangle
< 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) { 6, 41 }: Central Line L(6, 41) { 1, 371 }: Central Line L(1, 371) { 36, 372 }: Central Line L(36, 372) { 12, 590 }: Central Line L(12, 590) { 486, 499 }: Central Line L(486, 499) { 55, 1151 }: Central Line L(55, 1151) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_41 = -CEVA CONJUGATE OF X(31) (0.5823, 0.2244) X_1 = INCENTER (0.5714, 0.2333) X_371 = KENMOTU POINT (CONGRUENT SQUARES POINT) (0.5652, 0.2097) X_36 = INVERSE-IN-CIRCUMCIRCLE OF INCENTER (1.3333, 1.6330) X_372 = {X(3),X(6)}-HARMONIC CONJUGATE OF X(371) (0.7148, 0.4568) X_12 = {X(1),X(5)}-HARMONIC CONJUGATE OF X(11) (0.5641, 0.2407) X_590 = ISOGONAL CONJUGATE OF X(588) (0.6000, 0.2672) X_486 = INNER VECTEN POINT (-0.0810, -0.0170) X_499 = {X(1),X(2)}-HARMONIC CONJUGATE OF X(498) (0.4458, 0.1102) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_1151 = ISOGONAL CONJUGATE OF X(1131) (0.5483, 0.1819) X_2067 = POINT CAROLI II (0.5451, 0.1342) A B C X6 X41 X1 X371 X36 X372 X12 X590 X486 X499 X55 X1151 X2067 (a, b, c) = (5, 6, 7) | AB = 1

X2067 (POINT CAROLI II) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(- 1 + \sin A + \cos A : :\)
Search Value (6, 9, 13): \(-6.463549136011\)
▸ Alternate Coordinates2 forms

  • Trilinears: \((\cos A) (\cos B + \cos C + \sin A) : :\)

  • Trilinears: \(2 (\cos A) (\cos B + \cos C) + \sin 2A : :\)

▸ Incident Central Lines14 lines

{1, 371}, {3, 1335}, {6, 41}, {12, 590}, {27, 1659}, {36, 372}, {55, 1151}, {474, 1377}, {485, 1478}, {486, 499}, {603, 606}, {956, 1378}, {999, 1124}, {1790, 1805}

▸ Functional Relations3 relations