X3697

X631com(EXTOUCH TRIANGLE)

X3697 = excentral-to-ABC barycentric image of X631
< 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) { 10, 12 }: Central Line L(10, 12) { 8, 392 }: Central Line L(8, 392) { 200, 405 }: Central Line L(200, 405) { 37, 762 }: Central Line L(37, 762) { 936, 956 }: Central Line L(936, 956) { 518, 1698 }: Central Line L(518, 1698) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_12 = {X(1),X(5)}-HARMONIC CONJUGATE OF X(11) (0.5641, 0.2407) X_8 = NAGEL POINT (0.4694, 0.1333) X_392 = X(1,6)∩X(10,11) (0.5265, 0.1800) X_200 = -CEVA CONJUGATE OF X(9) (0.4392, 0.1037) X_405 = EULER LINE INTERCEPT OF LINE X(1)X(6) (0.5325, 0.1870) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_762 = TRILINEAR CUBE OF X(37) (0.5240, 0.1822) X_936 = INTERSECTION OF LINES X(1)X(2) AND X(3)X(9) (0.5138, 0.1768) X_956 = INTERSECTION OF LINES X(1)X(6) AND X(3)X(8) (0.4790, 0.1235) X_518 = ISOGONAL CONJUGATE OF X(105) (0.9154, 0.6489) X_1698 = INSIMILICENTER(BEVAN CIRCLE, NINE-POINTCIRCLE) (0.5306, 0.1933) X_3697 = com(EXTOUCH TRIANGLE) (0.5037, 0.1613) A B C X10 X12 X8 X392 X200 X405 X37 X762 X936 X956 X518 X1698 X3697 (a, b, c) = (5, 6, 7) | AB = 1

X3697 (X631com(EXTOUCH TRIANGLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Barycentrics: \(a (b+c) \cdot (a^{2}-b^{2}-4 b c-c^{2}) : :\)
Search Value (6, 9, 13): \(3.612733458104\)
▸ Linear Combinations1 combination
▸ Incident Central Lines16 lines

{2, 3555}, {8, 392}, {10, 12}, {37, 762}, {200, 405}, {474, 3361}, {517, 3091}, {518, 1698}, {756, 3214}, {936, 956}, {958, 3612}, {997, 1388}, {2551, 3419}, {3057, 3626}, {3219, 3579}, {3295, 3305}

▸ Functional Relations1 relation

  • X3697 = excentral-to-ABC barycentric image of X631