X813

o-(- 1, 1) CIRCUMCIRCLE POINT

X813 = trilinear pole of line X6X292
< 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) { 105, 238 }: Central Line L(105, 238) { 103, 295 }: Central Line L(103, 295) { 106, 292 }: Central Line L(106, 292) { 100, 649 }: Central Line L(100, 649) { 101, 667 }: Central Line L(101, 667) { 190, 789 }: Central Line L(190, 789) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_812 = ODD (- 1, 1) INFINITY POINT (0.1586, -0.2483) X_105 = Λ(INCENTER, SYMMEDIAN POINT) (0.9714, -0.0933) X_238 = -LINE CONJUGATE OF X(37) (1.6190, 1.4775) X_103 = ANTIPODE OF X(101) (0.7857, -0.3208) X_295 = ISOGONAL CONJUGATE OF X(242) (1.0582, 0.0142) X_106 = Λ(INCENTER, CENTROID) (1.0000, 0.0000) X_292 = -HIRST INVERSE OF X(291) (1.0127, 0.0417) X_100 = ANTICOMPLEMENT OF FEUERBACH POINT (0.1429, 0.4666) X_649 = CROSSDIFFERENCE OF X(1) and X(2) (-21.0000, 14.6969) X_101 = Ψ(INCENTER, SYMMEDIAN POINT) (0.2143, 0.5249) X_667 = CROSSDIFFERENCE OF X(2) AND X(37) (-6.1667, 5.7155) X_190 = YFF PARABOLIC POINT (0.0748, 0.3999) X_789 = o-(- 3, 0) CIRCUMCIRCLE POINT (0.0826, 0.3957) X_813 = o-(- 1, 1) CIRCUMCIRCLE POINT (0.9721, -0.0916) A B C X812 X105 X238 X103 X295 X106 X292 X100 X649 X101 X667 X190 X789 X813 (a, b, c) = (5, 6, 7) | AB = 1

X813 (o-(- 1, 1) CIRCUMCIRCLE POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(1/[a^{-2}(b^{1} - c^{1}) + a^{0}(b^{-1} - c ^{-1})] : :\)
Search Value (6, 9, 13): \(0.251971177091\)

X813 lies on the circumcircle.

▸ Incident Central Lines17 lines

{99, 1016}, {100, 649}, {101, 667}, {103, 295}, {105, 238}, {106, 292}, {163, 827}, {190, 789}, {334, 767}, {335, 675}, {644, 932}, {689, 799}, {692, 825}, {739, 902}, {765, 798}, {898, 1023}, {927, 1025}

▸ Functional Relations7 relations