X3083

INTERSECTION OF LINES X1X_2 AND X37X_494

For a construction and relationships to other points, see the preamble just before X37994.
< 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) { 1, 2 }: Nagel Line { 176, 329 }: Central Line L(176, 329) { 38, 494 }: Central Line L(38, 494) { 394, 1124 }: Central Line L(394, 1124) { 11, 1591 }: Central Line L(11, 1591) { 12, 1592 }: Central Line L(12, 1592) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_605 = INTERSECTION OF LINES X(371)X(602) AND X(372)X(601) (0.6106, 0.2829) X_1 = INCENTER (0.5714, 0.2333) X_2 = CENTROID (0.5374, 0.2000) X_176 = EQUAL DETOUR POINT (0.5803, 0.2537) X_329 = ISOTOMIC CONJUGATE OF X(189) (0.3847, -0.0222) X_38 = CROSSPOINT OF X(1) AND X(75) (0.5443, 0.1976) X_494 = 2nd VAN LAMOEN HOMOTHETIC CENTER (3.0897, 0.6637) X_394 = -CEVA CONJUGATE OF X(3) (0.3778, 0.0284) X_1124 = ISOGONAL CONJUGATE OF X(1123) (0.5846, 0.2489) X_11 = FEUERBACH POINT (0.7347, 0.0667) X_1591 = POINT CHARA III (0.5455, 0.2212) X_12 = {X(1),X(5)}-HARMONIC CONJUGATE OF X(11) (0.5641, 0.2407) X_1592 = POINT CHARA IV (0.4755, 0.0381) X_3083 = INTERSECTION OF LINES X(1)X(2) AND X(37)X(494) (0.5529, 0.2152) A B C X605 X1 X2 X176 X329 X38 X494 X394 X1124 X11 X1591 X12 X1592 X3083 (a, b, c) = (5, 6, 7) | AB = 1

X3083 (INTERSECTION OF LINES X1X_2 AND X37X_494) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(1 + \csc A : 1 + \csc B : 1 + \csc C\)
Barycentrics: \(abc + aS : abc + bS : abc + cS\)
Search Value (6, 9, 13): \(2.266684085765\)
▸ Alternate Coordinates1 form

  • Trilinears: \(bc + S : ca + S : ab + S\)

▸ Incident Central Lines14 lines

{1, 2}, {11, 1591}, {12, 1592}, {33, 1586}, {34, 1585}, {35, 1600}, {36, 1599}, {38, 494}, {55, 1584}, {56, 1583}, {176, 329}, {394, 1124}, {1038, 1590}, {1040, 1589}

▸ Functional Relations6 relations