X3997

X3735com[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, 213 }: Central Line L(10, 213) { 101, 171 }: Central Line L(101, 171) { 6, 519 }: Central Line L(6, 519) { 1, 672 }: Central Line L(1, 672) { 81, 644 }: Central Line L(81, 644) { 37, 758 }: Central Line L(37, 758) 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_213 = -CEVA CONJUGATE OF X(42) (0.6135, 0.2833) X_101 = Ψ(INCENTER, SYMMEDIAN POINT) (0.2143, 0.5249) X_171 = {X(2), X(31)}-HARMONIC CONJUGATE OF X(238) (0.5819, 0.2525) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_519 = ISOGONAL CONJUGATE OF X(106) (0.9566, 0.6107) X_1 = INCENTER (0.5714, 0.2333) X_672 = CROSSDIFFERENCE OF X(1) AND X(514) (1.9245, 2.2184) X_81 = CEVAPOINT OF INCENTER AND SYMMEDIAN POINT (0.5849, 0.2510) X_644 = TRILINEAR MULTIPLIER FOR YFF PARABOLA (-0.0171, 0.3359) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_758 = EVEN (1, 3) INFINITY POINT (0.1821, -0.2671) X_3997 = com[INVERSE(n(INCENTRAL TRIANGLE))] (0.5836, 0.2512) A B C X10 X213 X101 X171 X6 X519 X1 X672 X81 X644 X37 X758 X3997 (a, b, c) = (5, 6, 7) | AB = 1

X3997 (X3735com[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 \(f(a,b,c) = a(b + c)(2a^{2} + bc)\)
Search Value (6, 9, 13): \(1.381697966025\)
▸ Incident Central Lines13 lines

{1, 672}, {6, 519}, {10, 213}, {37, 758}, {42, 1018}, {44, 1573}, {58, 2329}, {81, 644}, {101, 171}, {386, 3501}, {551, 3230}, {1125, 2176}, {3625, 3780}