X1324

CIRCUMCIRCLE-INVERSE OF X10

X1324 is the circumcircle-inverse of X10.
< 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) { 3, 10 }: Central Line L(3, 10) { 58, 181 }: Central Line L(58, 181) { 35, 228 }: Central Line L(35, 228) { 98, 929 }: Central Line L(98, 929) { 36, 1054 }: Central Line L(36, 1054) { 759, 859 }: Central Line L(759, 859) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_58 = ISOGONAL CONJUGATE OF X(10) (0.6107, 0.2850) X_181 = APOLLONIUS POINT (0.6163, 0.3093) X_35 = {X(1),X(3)}-HARMONIC CONJUGATE OF X(36) (0.5373, 0.1706) X_228 = -CEVA CONJUGATE OF X(71) (0.5231, 0.1126) X_98 = TARRY POINT (0.8891, -0.2281) X_929 = ISOGONAL CONJUGATE OF X(928) (0.9516, 0.3396) X_36 = INVERSE-IN-CIRCUMCIRCLE OF INCENTER (1.3333, 1.6330) X_1054 = 6th SHARYGIN POINT (1.4286, -0.2333) X_759 = EVEN (1, 3) CIRCUMCIRCLE POINT (0.9498, -0.1389) X_859 = INTERCEPT OF EULER LINE AND TRILINEAR POLAR OF X(81) (1.1279, 1.7448) X_1324 = CIRCUMCIRCLE-INVERSE OF X(10) (1.2576, 3.1175) A B C X3 X10 X58 X181 X35 X228 X98 X929 X36 X1054 X759 X859 X1324 (a, b, c) = (5, 6, 7) | AB = 1

X1324 (CIRCUMCIRCLE-INVERSE OF X10) 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 \(f(a,b,c) = a[a^{5} - b^{5} - c^{5} + a^{3}bc - b^{3}ca - c^{3}ab + a^{2}b^{2}(b - a) + a^{2}c^{2}(c - a) + b^{2}c^{2}(b + c)]\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-3.014628607705\)
▸ Incident Central Lines6 lines

{3, 10}, {35, 228}, {36, 1054}, {58, 181}, {98, 929}, {759, 859}

▸ Functional Relations5 relations