X3096

INTERSECTION OF LINES X2X_32 AND X76X_141

X3096 = homothetic center of medial triangle and 5th Brocard triangle
< 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, 32 }: Central Line L(2, 32) { 76, 141 }: Central Line L(76, 141) { 114, 631 }: Central Line L(114, 631) { 316, 2076 }: Central Line L(316, 2076) { 211, 2979 }: Central Line L(211, 2979) { 4, 3098 }: Central Line L(4, 3098) 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_32 = 3rd POWER POINT (0.6400, 0.3332) X_76 = 3rd BROCARD POINT (0.4567, 0.1388) X_141 = COMPLEMENT OF SYMMEDIAN POINT (0.5061, 0.1663) X_114 = KIEPERT ANTIPODE (0.3616, 0.4140) X_631 = 3/5*OG (0.5224, 0.1608) X_316 = DROUSSENT PIVOT (-0.7850, -1.9118) X_2076 = INVERSE-IN-CIRCUMCIRCLE OF X(39) (1.3982, 1.5854) X_211 = -CEVA CONJUGATE OF X(39) (0.6801, 0.4536) X_2979 = CENTROID OF DUAL OF THE ORTHIC TRIANGLE (0.3937, -0.0373) X_4 = ORTHOCENTER (0.6122, 0.3958) X_3098 = INTERSECTION OF LINES X(3)X(6) AND X(69)X(74) (0.4500, 0.0195) X_3096 = INTERSECTION OF LINES X(2)X(32) AND X(76)X(141) (0.5156, 0.1716) A B C X2 X32 X76 X141 X114 X631 X316 X2076 X211 X2979 X4 X3098 X3096 (a, b, c) = (5, 6, 7) | AB = 1

X3096 (INTERSECTION OF LINES X2X_32 AND X76X_141) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(bc(b^{4} + c^{4} + b^{2}c^{2} + c^{2}a^{2} + a^{2}b^{2}) : :\)
Search Value (6, 9, 13): \(3.236406022496\)
▸ Incident Central Lines6 lines

{2, 32}, {4, 3098}, {76, 141}, {114, 631}, {211, 2979}, {316, 2076}

▸ Functional Relations4 relations

  • X3096 = complement of X7787

  • X3096 = {X15,X16}-harmonic conjugate of X32

  • X3096 = homothetic center of medial triangle and 5th Brocard triangle

  • X3096 = homothetic center of ABC and cross-triangle of ABC and 5th Brocard triangle