X3754

X5com[INVERSE(n(HEXYL TRIANGLE))]

X3754 = X389 of Fuhrmann 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, 12 }: Central Line L(10, 12) { 1, 88 }: Central Line L(1, 88) { 21, 484 }: Central Line L(21, 484) { 140, 517 }: Central Line L(140, 517) { 46, 993 }: Central Line L(46, 993) { 40, 1006 }: Central Line L(40, 1006) 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_12 = {X(1),X(5)}-HARMONIC CONJUGATE OF X(11) (0.5641, 0.2407) X_1 = INCENTER (0.5714, 0.2333) X_88 = ISOGONAL CONJUGATE OF X(44) (1.0000, 0.0000) X_21 = SCHIFFLER POINT (0.5287, 0.1771) X_484 = 1st EVANS PERSPECTOR (2.0952, 3.0327) X_140 = MIDPOINT OF X(3) AND X(5) (0.5281, 0.1755) X_517 = ISOGONAL CONJUGATE OF X(104) (0.8180, 0.7154) X_46 = -CEVA CONJUGATE OF X(1) (0.6917, 0.4543) X_993 = MIDPOINT OF X(1) AND X(63) (0.5140, 0.1578) X_40 = BEVAN POINT (0.4286, -0.0292) X_1006 = INTERCEPT OF EULER LINE AND LINEX(9)X(48) (0.5190, 0.1517) X_3754 = com[INVERSE(n(HEXYL TRIANGLE))] (0.5622, 0.2383) A B C X10 X12 X1 X88 X21 X484 X140 X517 X46 X993 X40 X1006 X3754 (a, b, c) = (5, 6, 7) | AB = 1

X3754 (X5com[INVERSE(n(HEXYL TRIANGLE))]) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Barycentrics: \(a(b + c)(a^{2} - b^{2} - c^{2} + 3bc) : :\)
Search Value (6, 9, 13): \(1.814312623755\)
▸ Linear Combinations1 combination
▸ Incident Central Lines22 lines

{1, 88}, {5, 2800}, {8, 2891}, {10, 12}, {21, 484}, {40, 1006}, {46, 993}, {80, 2475}, {140, 517}, {354, 3244}, {355, 2801}, {474, 2099}, {518, 3626}, {519, 942}, {551, 3057}, {860, 1825}, {997, 3340}, {1193, 1739}, {2295, 3125}, {2650, 3293}, {2975, 3336}, {3555, 3625}

▸ Functional Relations1 relation

Notes

Let OA be the circle centered at the A-vertex of the 2nd Conway triangle and passing through A; define OB and OC cyclically. X3754 is the radical center of OA, OB, OC. (Randy Hutson, August 28, 2020)