X3027

INCIRCLE-ANTIPODE OF X3023

X3027 is the incircle-antipode of X3023.
< 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) { 3023, 1 }: Central Line L(3023, 1) { 11, 114 }: Central Line L(11, 114) { 12, 115 }: Central Line L(12, 115) { 56, 99 }: Central Line L(56, 99) { 148, 388 }: Central Line L(148, 388) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3023 = 7th STEVANOVIC POINT (0.7493, 0.0823) X_1 = INCENTER (0.5714, 0.2333) X_11 = FEUERBACH POINT (0.7347, 0.0667) X_114 = KIEPERT ANTIPODE (0.3616, 0.4140) X_12 = {X(1),X(5)}-HARMONIC CONJUGATE OF X(11) (0.5641, 0.2407) X_115 = CENTER OF KIEPERT HYPERBOLA (0.7507, 0.0838) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_99 = STEINER POINT (0.1109, 0.4322) X_148 = STEINER POINT OF ANTICOMPLEMENTARY TRIANGLE (1.3904, -0.2646) X_388 = ∩X(7)X(8) (0.5790, 0.2635) X_3027 = INCIRCLE-ANTIPODE OF X(3023) (0.3936, 0.3842) A B C X3023 X1 X11 X114 X12 X115 X56 X99 X148 X388 X3027 (a, b, c) = (5, 6, 7) | AB = 1

X3027 (INCIRCLE-ANTIPODE OF X3023) 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 \(f(a,b,c) = bc(b + c)^{2}(a^{2} - bc)^{2}/(b + c - a)\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(0.928226813606\)

X3027 lies on the incircle.

▸ Incident Central Lines16 lines

{1, 2782}, {11, 114}, {12, 115}, {56, 99}, {65, 1356}, {147, 497}, {148, 388}, {192, 1916}, {226, 1365}, {350, 1281}, {553, 1357}, {690, 3028}, {950, 2784}, {1359, 2798}, {2023, 2276}, {2788, 3021}

▸ Functional Relations4 relations