X608

ISOGONAL CONJUGATE OF X345

X608 is the isogonal conjugate of X345.
< 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, 19 }: Central Line L(6, 19) { 7, 27 }: Central Line L(7, 27) { 25, 31 }: Central Line L(25, 31) { 223, 380 }: Central Line L(223, 380) { 109, 579 }: Central Line L(109, 579) { 193, 651 }: Central Line L(193, 651) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_345 = ISOTOMIC CONJUGATE OF X(278) (0.3405, 0.0381) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_19 = CLAWSON POINT (0.6246, 0.4244) X_7 = GERGONNE POINT (0.5903, 0.2769) X_27 = CEVAPOINT OF ORTHOCENTER AND CLAWSON CENTER (0.6182, 0.4112) X_25 = HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES (0.6329, 0.4497) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_223 = -CEVA CONJUGATE OF X(57) (0.4996, -0.0528) X_380 = INTERSECTION OF LINES X(1)X(19) AND X(9)X(55) (0.5631, 0.2035) X_109 = Ψ(INCENTER, CIRCUMCENTER) (0.3636, 0.5938) X_579 = HARMONIC OF X(284) (0.7212, 0.4674) X_193 = -CEVA CONJUGATE OF X(2) (0.7878, 0.4690) X_651 = TRILINEAR POLE OF LINE X(1)X(3) (0.3048, 0.5599) X_608 = ISOGONAL CONJUGATE OF X(345) (0.6361, 0.4975) A B C X345 X6 X19 X7 X27 X25 X31 X223 X380 X109 X579 X193 X651 X608 (a, b, c) = (5, 6, 7) | AB = 1

X608 (ISOGONAL CONJUGATE OF X345) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(a(1 - \sec A) : b(1 - \sec B) : c(1 - \sec c)\)
Barycentrics: \(a^{2}(1 - \sec A) : b^{2}(1 - \sec B) : c^{2}(1 - \sec C)\)
Search Value (6, 9, 13): \(-0.053535797359\)
▸ Alternate Coordinates1 form

  • Trilinears: \(\sin A - \tan A : :\)

▸ Incident Central Lines13 lines

{6, 19}, {7, 27}, {9, 1041}, {25, 31}, {28, 959}, {92, 894}, {108, 739}, {109, 579}, {193, 651}, {223, 380}, {240, 613}, {571, 913}, {604, 1042}

▸ Functional Relations4 relations

Notes

X608 is the vertex conjugate of the foci of the inconic that is the polar conjugate of the isotomic conjugate of the incircle. (Randy Hutson, October 15, 2018)

X608 is the {X6,X19}-harmonic conjugate of X607.