X614

INTERSECTION OF LINES X1X_2 AND X11X_33

X614 = crosssum of X42 and X72
< 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 { 11, 33 }: Central Line L(11, 33) { 9, 38 }: Central Line L(9, 38) { 22, 36 }: Central Line L(22, 36) { 25, 34 }: Central Line L(25, 34) { 31, 57 }: Central Line L(31, 57) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1 = INCENTER (0.5714, 0.2333) X_2 = CENTROID (0.5374, 0.2000) X_11 = FEUERBACH POINT (0.7347, 0.0667) X_33 = PERSPECTOR OF THE ORTHIC AND INTANGENTS TRIANGLES (0.6019, 0.3546) X_9 = MITTENPUNKT (0.5110, 0.1615) X_38 = CROSSPOINT OF X(1) AND X(75) (0.5443, 0.1976) X_22 = EXETER POINT (0.4143, -0.1221) X_36 = INVERSE-IN-CIRCUMCIRCLE OF INCENTER (1.3333, 1.6330) X_25 = HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES (0.6329, 0.4497) X_34 = -BETH CONJUGATE OF X(4) (0.6332, 0.4792) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_614 = INTERSECTION OF LINES X(1)X(2) AND X(11)X(33) (0.6310, 0.2916) A B C X1 X2 X11 X33 X9 X38 X22 X36 X25 X34 X31 X57 X614 (a, b, c) = (5, 6, 7) | AB = 1

X614 (INTERSECTION OF LINES X1X_2 AND X11X_33) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(a^{2} + b^{2} + c^{2} - 2bc\) (M. Iliev, 5/13/07)
Search Value (6, 9, 13): \(0.648337510477\)
▸ Alternate Coordinates4 forms

  • Trilinears: \(bc - S_{\omega } : ca - S_{\omega } : ab - S_{\omega }\) (C. Lozada, 9/07/2013)

  • Trilinears: \(\cot^{2}(B/2) + \cot^{2}(C/2) : :\)

  • Trilinears: \((1 - \cos A)(1 - \cos B \cos C) : :\)

  • Trilinears: \((1 - \sec A)(1 - \sec B \sec C) : :\)

▸ Incident Central Lines21 lines

{1, 2}, {6, 354}, {9, 38}, {11, 33}, {21, 988}, {22, 36}, {25, 34}, {31, 57}, {46, 595}, {63, 238}, {106, 998}, {165, 902}, {251, 609}, {269, 479}, {278, 1096}, {305, 350}, {394, 613}, {496, 1062}, {497, 1040}, {968, 1001}, {1616, 3057}

▸ Functional Relations4 relations