X3841

X3210com(4th EULER 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) { 10, 12 }: Central Line L(10, 12) { 2, 35 }: Central Line L(2, 35) { 5, 516 }: Central Line L(5, 516) { 377, 993 }: Central Line L(377, 993) { 535, 958 }: Central Line L(535, 958) { 759, 833 }: Central Line L(759, 833) 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_2 = CENTROID (0.5374, 0.2000) X_35 = {X(1),X(3)}-HARMONIC CONJUGATE OF X(36) (0.5373, 0.1706) X_5 = NINE-POINT CENTER (0.5561, 0.2489) X_516 = ISOGONAL CONJUGATE OF X(103) (0.7703, 0.7386) X_377 = EULER LINE INTERCEPT OF LINE X(7)X(8) (0.5473, 0.2258) X_993 = MIDPOINT OF X(1) AND X(63) (0.5140, 0.1578) X_535 = DIRECTION OF VECTOR AX + BX + CX, where X = X(36) (0.8224, 0.7130) X_958 = INTERSECTION OF LINES X(1)X(6) AND X(2)X(12) (0.5166, 0.1682) X_759 = EVEN (1, 3) CIRCUMCIRCLE POINT (0.9498, -0.1389) X_833 = o-(1, 4) CIRCUMCIRCLE POINT (0.1829, 0.5019) X_3841 = com(4th EULER TRIANGLE) (0.5374, 0.2057) A B C X10 X12 X2 X35 X5 X516 X377 X993 X535 X958 X759 X833 X3841 (a, b, c) = (5, 6, 7) | AB = 1

X3841 (X3210com(4th EULER TRIANGLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Barycentrics: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = (b + c)(b^{3} + c^{3} - a^{2}b - a^{2}c - b^{2}c - bc^{2} - 3abc)\)
Search Value (6, 9, 13): \(2.522313518534\)
▸ Incident Central Lines12 lines

{2, 35}, {5, 516}, {10, 12}, {79, 3219}, {377, 993}, {484, 1698}, {495, 3626}, {496, 1125}, {535, 958}, {626, 3739}, {759, 833}, {1770, 3647}