X3991

X1212com[INVERSE(n(INCENTRAL 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) { 10, 37 }: Central Line L(10, 37) { 1, 728 }: Central Line L(1, 728) { 65, 1018 }: Central Line L(65, 1018) { 72, 1334 }: Central Line L(72, 1334) { 519, 1212 }: Central Line L(519, 1212) { 44, 2241 }: Central Line L(44, 2241) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_1 = INCENTER (0.5714, 0.2333) X_728 = INTERSECTION OF LINES X(8)X(9) AND X(57)X(345) (0.3648, 0.0624) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_1018 = -CROSS CONJUGATE OF X(1) (0.1051, 0.4358) X_72 = ISOGONAL CONJUGATE OF X(28) (0.4367, 0.0733) X_1334 = POINT ALYA (0.5324, 0.1760) X_519 = ISOGONAL CONJUGATE OF X(106) (0.9566, 0.6107) X_1212 = ISOGONAL CONJUGATE OF X(1170) (0.5256, 0.1789) X_44 = -LINE CONJUGATE OF X(1) (2.1429, 2.0996) X_2241 = -ISOCONJUGATE OF X(749) (0.4799, 0.0999) X_3991 = com[INVERSE(n(INCENTRAL TRIANGLE))] (0.6337, 0.2848) A B C X10 X37 X1 X728 X65 X1018 X72 X1334 X519 X1212 X44 X2241 X3991 (a, b, c) = (5, 6, 7) | AB = 1

X3991 (X1212com[INVERSE(n(INCENTRAL TRIANGLE))]) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Barycentrics: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = a(b + c)(a^{2} + b^{2} + c^{2} - 2ab - 2ac)\)
Search Value (6, 9, 13): \(-0.849920633725\)
▸ Incident Central Lines14 lines

{1, 728}, {9, 3295}, {10, 37}, {44, 2241}, {65, 1018}, {72, 1334}, {192, 3673}, {210, 3294}, {517, 3208}, {518, 3730}, {519, 1212}, {672, 3555}, {942, 3501}, {3509, 3579}