X2055

ORION TRANSFORM OF X3

X2055 is the perspector of triangle ABC and the orthic triangle of the cevian triangle of the circumcenter. (Randy Hutson, 9/23/2011)
< A B C >: Reference Triangle △ABC < P_a P_b P_c >: Cevian Triangle △P_a P_b P_c [ A B ]: Sideline AB (Base c = 1) [ B C ]: Sideline BC (Side a) [ C A ]: Sideline CA (Side b) [ A P_a ]: A-Cevian A–P_a [ B P_b ]: B-Cevian B–P_b [ C P_c ]: C-Cevian C–P_c { 3, 6 }: Brocard Axis { 5, 275 }: Central Line L(5, 275) { 54, 418 }: Central Line L(54, 418) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) P_a = Cevian Trace P_a on BC (1.1339, -0.2072) P_b = Cevian Trace P_b on CA (-0.1383, -0.1355) P_c = Cevian Trace P_c on AB (0.4179, 0.0000) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_5 = NINE-POINT CENTER (0.5561, 0.2489) X_275 = CEVAPOINT OF ORTHOCENTER AND SYMMEDIAN POINT (0.6057, 0.3473) X_54 = KOSNITA POINT (0.5880, 0.2176) X_418 = -CEVA-CONJUGATE OF X(216) (0.4854, 0.0640) X_2055 = ORION TRANSFORM OF X(3) (0.3946, -0.0721) A B C Pa Pb Pc X3 X6 X5 X275 X54 X418 X2055 (a, b, c) = (5, 6, 7) | AB = 1

X2055 (ORION TRANSFORM OF X3) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

  • Derived Triangle: Cevian Triangle △PaPbPc — vertices Pa, Pb, Pc (Traces of cevians through target center on BC, CA, AB)

  • Concurrence Lines: A–Pa, B–Pb, C–Pc concurring at X2055

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where f(a,b,c) is given just above X2055, using X = X3
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-0.172128039314\)
▸ Incident Central Lines3 lines

{3, 6}, {5, 275}, {54, 418}