X3285

INTERSECTION OF LINES X3X_6 AND X21X_45

Let L denote the line through X10 perpendicular to the Euler line. Coefficients for a trilinear equation for L are the trilinears for X3285.
< 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) { 3, 6 }: Brocard Axis { 21, 45 }: Central Line L(21, 45) { 81, 89 }: Central Line L(81, 89) { 112, 953 }: Central Line L(112, 953) { 649, 834 }: Central Line L(649, 834) { 55, 2206 }: Central Line L(55, 2206) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_902 = CROSSPOINT OF X(6) AND X(106) (1.2500, 1.2247) X_2251 = -ISOCONJUGATE OF X(903) (0.9633, 0.9438) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_21 = SCHIFFLER POINT (0.5287, 0.1771) X_45 = -BETH CONJUGATE OF X(1) (0.5418, 0.1981) X_81 = CEVAPOINT OF INCENTER AND SYMMEDIAN POINT (0.5849, 0.2510) X_89 = ISOGONAL CONJUGATE OF X(45) (0.5963, 0.2697) X_112 = Ψ(ORTHOCENTER, SYMMEDIAN POINT) (0.5162, 0.6121) X_953 = ISOGONAL CONJUGATE OF X(952) (0.0000, 0.2041) X_649 = CROSSDIFFERENCE OF X(1) and X(2) (-21.0000, 14.6969) X_834 = ODD (2, 3) INFINITY POINT (1.0367, -0.1085) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_2206 = -ISOCONJUGATE OF X(321) (0.6455, 0.3498) X_3285 = INTERSECTION OF LINES X(3)X(6) AND X(21)X(45) (1.0773, 1.0556) A B C X902 X2251 X3 X6 X21 X45 X81 X89 X112 X953 X649 X834 X55 X2206 X3285 (a, b, c) = (5, 6, 7) | AB = 1

X3285 (INTERSECTION OF LINES X3X_6 AND X21X_45) 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 \(f(a,b,c) = a(2a - b - c)/(b + c)\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-1.249466931274\)
▸ Incident Central Lines8 lines

{3, 6}, {21, 45}, {44, 2251}, {55, 2206}, {81, 89}, {110, 2384}, {112, 953}, {649, 834}

▸ Functional Relations5 relations