X3358

MIDPOINT OF X9 AND X84

X3358 is the midpoint of X9 and X84.
< 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) { 9, 84 }: Central Line L(9, 84) { 3, 9 }: Central Line L(3, 9) { 11, 57 }: Central Line L(11, 57) { 4, 1445 }: Central Line L(4, 1445) { 516, 1158 }: Central Line L(516, 1158) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_9 = MITTENPUNKT (0.5110, 0.1615) X_84 = ISOGONAL CONJUGATE OF X(40) (0.6071, 0.6816) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_11 = FEUERBACH POINT (0.7347, 0.0667) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_4 = ORTHOCENTER (0.6122, 0.3958) X_1445 = -BETH CONJUGATE OF X(344) (0.6570, 0.3740) X_516 = ISOGONAL CONJUGATE OF X(103) (0.7703, 0.7386) X_1158 = CIRCUMCENTER OF EXTOUCH TRIANGLE (0.5179, 0.3262) X_3358 = MIDPOINT OF X(9) AND X(84) (0.5591, 0.4216) A B C X9 X84 X3 X11 X57 X4 X1445 X516 X1158 X3358 (a, b, c) = (5, 6, 7) | AB = 1

X3358 (MIDPOINT OF X9 AND X84) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = x_{9} + x_{84} (using actual trilinear distances)\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-24.599201261600\)
▸ Linear Combinations1 combination
▸ Incident Central Lines5 lines

{3, 9}, {4, 1445}, {11, 57}, {516, 1158}, {954, 1071}

▸ Functional Relations1 relation