X3296

ISOGONAL CONJUGATE OF X3295

X3296 is the isogonal conjugate of X3295.
< 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) { 4, 354 }: Central Line L(4, 354) { 1, 376 }: Central Line L(1, 376) { 80, 388 }: Central Line L(80, 388) { 79, 497 }: Central Line L(79, 497) { 21, 999 }: Central Line L(21, 999) { 7, 1058 }: Central Line L(7, 1058) 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_3338 = INTERSECTION OF LINES X(1)X(3) AND X(7)X(90) (0.5971, 0.2805) X_4 = ORTHOCENTER (0.6122, 0.3958) X_354 = WEILL POINT (0.5823, 0.2533) X_376 = CENTROID OF THE ANTIPEDAL TRIANGLE OF X(2) (0.4626, 0.0042) X_80 = REFLECTION OF INCENTER IN FEUERBACH POINT (0.8980, -0.1000) X_388 = ∩X(7)X(8) (0.5790, 0.2635) X_79 = ISOGONAL CONJUGATE OF X(35) (0.5976, 0.3019) X_497 = CROSSPOINT OF GERGONNE POINT AND NAGEL POINT (0.5593, 0.1851) X_21 = SCHIFFLER POINT (0.5287, 0.1771) X_999 = MIDPOINT OF X(1) AND X(57) (0.5926, 0.2722) X_7 = GERGONNE POINT (0.5903, 0.2769) X_1058 = POINT ALKALUROPS (0.5662, 0.2123) X_3296 = ISOGONAL CONJUGATE OF X(3295) (0.5834, 0.2585) A B C X1 X3338 X4 X354 X376 X80 X388 X79 X497 X21 X999 X7 X1058 X3296 (a, b, c) = (5, 6, 7) | AB = 1

X3296 (ISOGONAL CONJUGATE OF X3295) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(1/(2 + \cos A) : 1/(2 + \cos B) : 1/(2 + \cos C)\)
Barycentrics: \((\sin A)/(2 + \cos A) : :\)
Search Value (6, 9, 13): \(1.173344008817\)
▸ Incident Central Lines9 lines

{1, 376}, {4, 354}, {7, 1058}, {21, 999}, {65, 1000}, {79, 497}, {80, 388}, {443, 942}, {1039, 1870}

▸ Functional Relations4 relations

Notes

Let A' be the midpoint of X1 and the A-intouch point. Define B' and C' cyclically. The lines AA', BB', CC' concur in X3296. (Randy Hutson, January 15, 2019)