X3028

INCIRCLE-ANTIPODE OF X3024

X3028 is the incircle-antipode of X3024.
< 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) { 3024, 1 }: Central Line L(3024, 1) { 11, 113 }: Central Line L(11, 113) { 12, 125 }: Central Line L(12, 125) { 56, 110 }: Central Line L(56, 110) { 146, 497 }: Central Line L(146, 497) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3024 = 8th STEVANOVIC POINT (0.6850, 0.0295) X_1 = INCENTER (0.5714, 0.2333) X_11 = FEUERBACH POINT (0.7347, 0.0667) X_113 = JERABEK ANTIPODE (0.4319, 0.4718) X_12 = {X(1),X(5)}-HARMONIC CONJUGATE OF X(11) (0.5641, 0.2407) X_125 = CENTER OF JERABEK HYPERBOLA (0.6803, 0.0260) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_110 = FOCUS OF KIEPERT PARABOLA (0.2516, 0.5478) X_146 = REFLECTION OF X(20) IN X(110) (0.1155, 1.2873) X_497 = CROSSPOINT OF GERGONNE POINT AND NAGEL POINT (0.5593, 0.1851) X_3028 = INCIRCLE-ANTIPODE OF X(3024) (0.4579, 0.4371) A B C X3024 X1 X11 X113 X12 X125 X56 X110 X146 X497 X3028 (a, b, c) = (5, 6, 7) | AB = 1

X3028 (INCIRCLE-ANTIPODE OF X3024) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = bc(b + c)^{2}(1 - 2 \cos A)^{2}/(b + c - a)\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(0.351322772683\)

X3028 lies on the incircle.

▸ Incident Central Lines17 lines

{1, 3024}, {11, 113}, {12, 125}, {34, 1112}, {36, 1464}, {56, 110}, {57, 2948}, {65, 1365}, {146, 497}, {690, 3027}, {1359, 2850}, {1367, 1439}, {1469, 2854}, {1870, 1986}, {2646, 2779}, {2772, 3022}, {2775, 3021}

▸ Functional Relations5 relations