X3024

8th STEVANOVIC POINT

X3024 = reflection of X3028 in X1
< 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) { 3028, 1 }: Central Line L(3028, 1) { 12, 113 }: Central Line L(12, 113) { 56, 74 }: Central Line L(56, 74) { 11, 125 }: Central Line L(11, 125) { 146, 388 }: Central Line L(146, 388) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3028 = INCIRCLE-ANTIPODE OF X(3024) (0.4579, 0.4371) X_1 = INCENTER (0.5714, 0.2333) X_12 = {X(1),X(5)}-HARMONIC CONJUGATE OF X(11) (0.5641, 0.2407) X_113 = JERABEK ANTIPODE (0.4319, 0.4718) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_74 = ISOGONAL CONJUGATE OF EULER INFINITY POINT (0.7484, -0.3437) X_11 = FEUERBACH POINT (0.7347, 0.0667) X_125 = CENTER OF JERABEK HYPERBOLA (0.6803, 0.0260) X_146 = REFLECTION OF X(20) IN X(110) (0.1155, 1.2873) X_388 = ∩X(7)X(8) (0.5790, 0.2635) X_3024 = 8th STEVANOVIC POINT (0.6850, 0.0295) A B C X3028 X1 X12 X113 X56 X74 X11 X125 X146 X388 X3024 (a, b, c) = (5, 6, 7) | AB = 1

X3024 (8th STEVANOVIC POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(a(b + c - a)(b - c)^{2}(b^{2} + c^{2} - a^{2} + bc)^{2} : :\)
Search Value (6, 9, 13): \(3.029294246231\)

X3024 lies on the incircle.

▸ Incident Central Lines16 lines

{1, 3028}, {11, 125}, {12, 113}, {33, 1112}, {35, 1511}, {56, 74}, {65, 1354}, {146, 388}, {690, 3023}, {1317, 2771}, {1359, 2778}, {1361, 2779}, {1469, 2781}, {1682, 3031}, {2774, 3022}, {2836, 3021}

▸ Functional Relations6 relations

Notes

The circumcircle of the incentral triangle intersects the incircle in 2 points, X11 and X3024. (Randy Hutson, August 29, 2018)