X3058

INTERSECTION OF LINES X1X_30 AND X2X_11

X3058 = X2-of-Mandart-incircle-triangle
< 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) { 2, 11 }: Central Line L(2, 11) { 1, 30 }: Central Line L(1, 30) { 12, 381 }: Central Line L(12, 381) { 72, 519 }: Central Line L(72, 519) { 496, 549 }: Central Line L(496, 549) { 516, 553 }: Central Line L(516, 553) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2 = CENTROID (0.5374, 0.2000) X_11 = FEUERBACH POINT (0.7347, 0.0667) X_1 = INCENTER (0.5714, 0.2333) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_12 = {X(1),X(5)}-HARMONIC CONJUGATE OF X(11) (0.5641, 0.2407) X_381 = MIDPOINT OF X(2) AND X(4) (0.5748, 0.2979) X_72 = ISOGONAL CONJUGATE OF X(28) (0.4367, 0.0733) X_519 = ISOGONAL CONJUGATE OF X(106) (0.9566, 0.6107) X_496 = {X(1),X(5)}-HARMONIC CONJUGATE OF X(495) (0.5843, 0.2201) X_549 = MIDPOINT OF X(2) AND X(3) (0.5187, 0.1510) X_516 = ISOGONAL CONJUGATE OF X(103) (0.7703, 0.7386) X_553 = POINT MAIA II (0.5963, 0.2857) X_3058 = INTERSECTION OF LINES X(1)X(30) AND X(2)X(11) (0.5543, 0.1885) A B C X2 X11 X1 X30 X12 X381 X72 X519 X496 X549 X516 X553 X3058 (a, b, c) = (5, 6, 7) | AB = 1

X3058 (INTERSECTION OF LINES X1X_30 AND X2X_11) 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 \(f(a,b,c) = bc(b + c - a)(2a^{2} + b^{2} + c^{2} - 2bc)\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(2.636859871670\)
▸ Linear Combinations1 combination
▸ Incident Central Lines15 lines

{1, 30}, {2, 11}, {12, 381}, {72, 519}, {376, 1250}, {496, 549}, {516, 553}, {529, 2098}, {541, 3028}, {542, 3024}, {543, 3023}, {544, 3022}, {551, 2646}, {595, 3017}, {597, 2330}

▸ Functional Relations3 relations