X3980

X612com(1st BROCARD TRIANGLE)

X3980 = X612-of-1st-Brocard-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, 46 }: Central Line L(10, 46) { 75, 171 }: Central Line L(75, 171) { 2, 846 }: Central Line L(2, 846) { 43, 894 }: Central Line L(43, 894) { 321, 750 }: Central Line L(321, 750) { 612, 726 }: Central Line L(612, 726) 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_46 = -CEVA CONJUGATE OF X(1) (0.6917, 0.4543) X_75 = ISOTOMIC CONJUGATE OF INCENTER (0.4988, 0.1682) X_171 = {X(2), X(31)}-HARMONIC CONJUGATE OF X(238) (0.5819, 0.2525) X_2 = CENTROID (0.5374, 0.2000) X_846 = 4th SHARYGIN POINT (0.5437, 0.1969) X_43 = -CEVA CONJUGATE OF X(1) (0.6358, 0.2963) X_894 = ISOGONAL CONJUGATE OF X(893) (0.5501, 0.2184) X_321 = ISOTOMIC CONJUGATE OF X(81) (0.4800, 0.1527) X_750 = INTERSECTION OF LINES X(1)X(88) AND X(2)X(31) (0.5675, 0.2354) X_612 = INTERSECTION OF LINES X(1)X(2) AND X(9)X(31) (0.5582, 0.2203) X_726 = EVEN (- 2, -1) INFINITY POINT (1.0187, 0.5358) X_3980 = com(1st BROCARD TRIANGLE) (0.5325, 0.2024) A B C X10 X46 X75 X171 X2 X846 X43 X894 X321 X750 X612 X726 X3980 (a, b, c) = (5, 6, 7) | AB = 1

X3980 (X612com(1st BROCARD 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 \(f(a,b,c) = a^{3} + b^{2}c + bc^{2} + 2abc\)
Search Value (6, 9, 13): \(2.707260077504\)
▸ Incident Central Lines15 lines

{1, 3210}, {2, 846}, {10, 46}, {43, 894}, {57, 3741}, {75, 171}, {192, 1961}, {321, 750}, {612, 726}, {740, 940}, {968, 1125}, {986, 1010}, {1215, 1376}, {2345, 3509}, {3550, 3757}

▸ Functional Relations1 relation