X950

CROSSPOINT OF X8 AND X29

X950 is the crosspoint of X8 and X29.
< 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, 4 }: Incenter–Orthocenter Line { 8, 9 }: Central Line L(8, 9) { 10, 55 }: Central Line L(10, 55) { 20, 57 }: Central Line L(20, 57) { 11, 214 }: Central Line L(11, 214) { 29, 284 }: Central Line L(29, 284) 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_29 = CEVAPOINT OF INCENTER AND ORTHOCENTER (0.5903, 0.3384) X_1 = INCENTER (0.5714, 0.2333) X_4 = ORTHOCENTER (0.6122, 0.3958) X_9 = MITTENPUNKT (0.5110, 0.1615) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_20 = DE LONGCHAMPS POINT (0.3878, -0.1916) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_11 = FEUERBACH POINT (0.7347, 0.0667) X_214 = -CEVA CONJUGATE OF X(44) (0.3571, 0.3499) X_284 = -CROSS CONJUGATE OF X(21) (0.5646, 0.2088) X_950 = CROSSPOINT OF X(8) AND X(29) (0.5621, 0.1961) A B C X8 X29 X1 X4 X9 X10 X55 X20 X57 X11 X214 X284 X950 (a, b, c) = (5, 6, 7) | AB = 1

X950 (CROSSPOINT OF X8 AND X29) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(bc(b + c - a)[2a^{3} + (b + c)(a^{2} + (b - c)^{2})] : :\)
Search Value (6, 9, 13): \(2.529844454800\)
▸ Incident Central Lines17 lines

{1, 4}, {8, 9}, {10, 55}, {11, 214}, {20, 57}, {29, 284}, {30, 553}, {35, 1006}, {65, 516}, {72, 519}, {80, 943}, {142, 377}, {145, 329}, {281, 380}, {389, 517}, {440, 1104}, {947, 1067}

▸ Functional Relations6 relations

Notes

Let A'B'C' be the Gergonne line extraversion triangle, as defined at X10180. Let La be the reflection of line BC in line B'C', and define Lb and Lc cyclically. Let A″ = Lb ∩ Lc, and define B″ and C″ cyclically. The lines AA″, BB″, CC″ concur in X950. (Randy Hutson, January 29, 2018)