X812

ODD (- 1, 1) INFINITY POINT

As the isogonal conjugate of a point on the circumcircle, X812 lies on the line at infinity.
< 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) { 30, 511 }: Central Line L(30, 511) { 190, 646 }: Central Line L(190, 646) { 649, 693 }: Central Line L(649, 693) { 673, 1024 }: Central Line L(673, 1024) { 1015, 1086 }: Central Line L(1015, 1086) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_813 = o-(- 1, 1) CIRCUMCIRCLE POINT (0.9721, -0.0916) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_511 = ISOGONAL CONJUGATE OF X(98) (0.2335, -0.3020) X_190 = YFF PARABOLIC POINT (0.0748, 0.3999) X_646 = BARYCENTRIC MULTIPLIER FOR YFF PARABOLA (-0.0898, 0.2051) X_649 = CROSSDIFFERENCE OF X(1) and X(2) (-21.0000, 14.6969) X_693 = ISOTOMIC CONJUGATE OF X(100) (-25.8163, 8.9981) X_673 = TRILINEAR POLE OF LINE X(1)X(514) (0.9471, -0.0769) X_1024 = INTERSECTION OF LINES X(6)X(513) ANDX(9)X(522) (1.0370, 0.0294) X_1015 = EXSIMILICENTER OF MOSES CIRCLE AND INCIRCLE (0.7982, 0.1348) X_1086 = CENTER OF HYPERBOLA {{A,B,C,X(2),X(7)|} (0.7687, 0.1000) X_812 = ODD (- 1, 1) INFINITY POINT (0.1586, -0.2483) A B C X813 X30 X511 X190 X646 X649 X693 X673 X1024 X1015 X1086 X812 (a, b, c) = (5, 6, 7) | AB = 1

X812 (ODD (- 1, 1) INFINITY POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(a ^{-2}(b^{1} - c^{1}) + a^{0}(b ^{-1} - c ^{-1}) : :\)
Barycentrics: \((b - c) (a^{2} - b c) : :\)
▸ Incident Central Lines6 lines

{30, 511}, {190, 646}, {649, 693}, {673, 1024}, {903, 1022}, {1015, 1086}

▸ Functional Relations10 relations