X789

o-(- 3, 0) CIRCUMCIRCLE POINT

X789 = intersection, other than A, B, C, of circumcircle and hyperbola {A, B, C,PU(6)}}
< 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) { 6, 717 }: Central Line L(6, 717) { 1, 731 }: Central Line L(1, 731) { 31, 701 }: Central Line L(31, 701) { 2, 743 }: Central Line L(2, 743) { 101, 668 }: Central Line L(101, 668) { 86, 741 }: Central Line L(86, 741) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_788 = ODD (- 3, 0) INFINITY POINT (1.0251, -0.1264) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_717 = EVEN (- 3, 0) CIRCUMCIRCLE POINT (1.0062, 0.1664) X_1 = INCENTER (0.5714, 0.2333) X_731 = EVEN (- 2, 1) CIRCUMCIRCLE POINT (1.0101, 0.0876) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_701 = EVEN (- 4, - 1) CIRCUMCIRCLE POINT (0.9924, 0.2359) X_2 = CENTROID (0.5374, 0.2000) X_743 = EVEN (- 1, 2) CIRCUMCIRCLE POINT (1.0002, 0.0008) X_101 = Ψ(INCENTER, SYMMEDIAN POINT) (0.2143, 0.5249) X_668 = TRILINEAR POLE OF LINE X(2)X(37) (0.0159, 0.3302) X_86 = CEVAPOINT OF INCENTER AND CENTROID (0.5534, 0.2171) X_741 = EVEN (- 1, 1) CIRCUMCIRCLE POINT (1.0071, 0.0451) X_789 = o-(- 3, 0) CIRCUMCIRCLE POINT (0.0826, 0.3957) A B C X788 X6 X717 X1 X731 X31 X701 X2 X743 X101 X668 X86 X741 X789 (a, b, c) = (5, 6, 7) | AB = 1

X789 (o-(- 3, 0) CIRCUMCIRCLE POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(a ^{- 2}/(b^{3} - c^{3}) : :\)
Search Value (6, 9, 13): \(4.318201239439\)

X789 lies on the circumcircle.

▸ Incident Central Lines15 lines

{1, 731}, {2, 743}, {6, 717}, {31, 701}, {75, 753}, {76, 761}, {86, 741}, {100, 874}, {101, 668}, {106, 870}, {110, 799}, {112, 811}, {190, 813}, {675, 871}, {727, 985}

▸ Functional Relations6 relations

Notes

As the trilinear product of Steiner circumellipse antipodes, X789 lies on conic {A, B, C,X668,X789}} with center X6376 and perspector X75. (Randy Hutson, July 11, 2019)