X2002

ORTHOCORRESPONDENT OF X33

< 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) { 2, 7 }: Centroid–Gergonne Line { 19, 77 }: Central Line L(19, 77) { 85, 653 }: Central Line L(85, 653) { 169, 651 }: Central Line L(169, 651) { 36, 990 }: Central Line L(36, 990) { 1, 1813 }: Central Line L(1, 1813) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2 = CENTROID (0.5374, 0.2000) X_7 = GERGONNE POINT (0.5903, 0.2769) X_19 = CLAWSON POINT (0.6246, 0.4244) X_77 = ISOGONAL CONJUGATE OF X(33) (0.5270, 0.1305) X_85 = ISOTOMIC CONJUGATE OF X(9) (0.5610, 0.2421) X_653 = TRILINEAR POLE OF LINE X(1)X(4) (0.5097, 0.6030) X_169 = -CEVA CONJUGATE OF X(1) (0.5497, 0.2510) X_651 = TRILINEAR POLE OF LINE X(1)X(3) (0.3048, 0.5599) X_36 = INVERSE-IN-CIRCUMCIRCLE OF INCENTER (1.3333, 1.6330) X_990 = INTERSECTION OF LINES X(1)X(7) AND X(3)X(37) (0.6104, 0.3234) X_1 = INCENTER (0.5714, 0.2333) X_1813 = INVERSE MIMOSA TRANSFORM OF X(650) (-0.1088, 0.3999) X_2002 = ORTHOCORRESPONDENT OF X(33) (0.5619, 0.2356) A B C X2 X7 X19 X77 X85 X653 X169 X651 X36 X990 X1 X1813 X2002 (a, b, c) = (5, 6, 7) | AB = 1

X2002 (ORTHOCORRESPONDENT OF X33) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = yz + (-x \cos A + y \cos B + z \cos C)x\), where \(x : y : z\) = X33
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(625.225813288983\)
▸ Incident Central Lines8 lines

{1, 1813}, {2, 7}, {19, 77}, {36, 990}, {85, 653}, {169, 651}, {269, 1781}, {1172, 1790}