X3099

INTERSECTION OF LINES X1X_32 AND X846X_902

< 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) { 1, 32 }: Central Line L(1, 32) { 846, 902 }: Central Line L(846, 902) { 672, 1282 }: Central Line L(672, 1282) { 518, 2076 }: Central Line L(518, 2076) { 10, 2896 }: Central Line L(10, 2896) { 726, 2959 }: Central Line L(726, 2959) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1 = INCENTER (0.5714, 0.2333) X_32 = 3rd POWER POINT (0.6400, 0.3332) X_846 = 4th SHARYGIN POINT (0.5437, 0.1969) X_902 = CROSSPOINT OF X(6) AND X(106) (1.2500, 1.2247) X_672 = CROSSDIFFERENCE OF X(1) AND X(514) (1.9245, 2.2184) X_1282 = 5th SHARYGIN POINT (-0.1429, 0.8165) X_518 = ISOGONAL CONJUGATE OF X(105) (0.9154, 0.6489) X_2076 = INVERSE-IN-CIRCUMCIRCLE OF X(39) (1.3982, 1.5854) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_2896 = ANTICOMPLEMENTARY CONJUGATE OF X(76) (0.4820, 0.1279) X_726 = EVEN (- 2, -1) INFINITY POINT (1.0187, 0.5358) X_2959 = EXCENTRAL-ISOGONAL CONJUGATE OF X(147) (1.6903, 2.0547) X_3099 = INTERSECTION OF LINES X(1)X(32) AND X(846)X(902) (1.9400, 2.2289) A B C X1 X32 X846 X902 X672 X1282 X518 X2076 X10 X2896 X726 X2959 X3099 (a, b, c) = (5, 6, 7) | AB = 1

X3099 (INTERSECTION OF LINES X1X_32 AND X846X_902) 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 \(f(a,b,c) = (b^{4} + c^{4} - a^{4} - 2a^{3}b - 2a^{3}c + b^{2}c^{2} + c^{2}a^{2} + a^{2}b^{2})\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-5.787973875598\)
▸ Incident Central Lines6 lines

{1, 32}, {10, 2896}, {518, 2076}, {672, 1282}, {726, 2959}, {846, 902}