X3023

7th STEVANOVIC POINT

X3023 = reflection of X3027 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) { 3027, 1 }: Central Line L(3027, 1) { 11, 115 }: Central Line L(11, 115) { 12, 114 }: Central Line L(12, 114) { 56, 98 }: Central Line L(56, 98) { 147, 388 }: Central Line L(147, 388) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3027 = INCIRCLE-ANTIPODE OF X(3023) (0.3936, 0.3842) X_1 = INCENTER (0.5714, 0.2333) X_11 = FEUERBACH POINT (0.7347, 0.0667) X_115 = CENTER OF KIEPERT HYPERBOLA (0.7507, 0.0838) X_12 = {X(1),X(5)}-HARMONIC CONJUGATE OF X(11) (0.5641, 0.2407) X_114 = KIEPERT ANTIPODE (0.3616, 0.4140) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_98 = TARRY POINT (0.8891, -0.2281) X_147 = TARRY POINT OF ANTICOMPLEMENTARY TRIANGLE (-0.1660, 1.0561) X_388 = ∩X(7)X(8) (0.5790, 0.2635) X_3023 = 7th STEVANOVIC POINT (0.7493, 0.0823) A B C X3027 X1 X11 X115 X12 X114 X56 X98 X147 X388 X3023 (a, b, c) = (5, 6, 7) | AB = 1

X3023 (7th STEVANOVIC POINT) 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 \(f(a,b,c) = bc(b + c - a)(b - c)^{2}(a^{2} + bc)^{2}\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(2.452390205308\)

X3023 lies on the incircle.

▸ Incident Central Lines17 lines

{1, 2782}, {11, 115}, {12, 114}, {56, 98}, {65, 1355}, {147, 388}, {148, 497}, {330, 1916}, {690, 3024}, {1317, 2783}, {1359, 2791}, {1361, 2792}, {1500, 1569}, {1682, 3029}, {2023, 2275}, {2786, 3022}, {2795, 3021}

▸ Functional Relations3 relations