X1639

TRIPOLAR CENTROID OF X8

X1639 is the tripolar centroid of X8.
< 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) { 1638, 2 }: Central Line L(1638, 2) { 9, 654 }: Central Line L(9, 654) { 2, 918 }: Central Line L(2, 918) { 210, 926 }: Central Line L(210, 926) { 11, 1146 }: Central Line L(11, 1146) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1638 = TRIPOLAR CENTROID OF X(7) (1.6871, 0.9998) X_2 = CENTROID (0.5374, 0.2000) X_9 = MITTENPUNKT (0.5110, 0.1615) X_654 = CROSSDIFFERENCE OF X(1) AND X(5) (2.8235, 1.7291) X_918 = ISOTOMIC CONJUGATE OF X(666) (1.0192, 0.5351) X_210 = -CEVA CONJUGATE OF X(37) (0.4925, 0.1466) X_926 = CROSSDIFFERENCE OF X(6) AND X(7) (0.0512, -0.1286) X_11 = FEUERBACH POINT (0.7347, 0.0667) X_1146 = CENTER OF HYPERBOLA {{A,B,C,X(2),X(8)}} (0.6866, 0.0428) X_1639 = TRIPOLAR CENTROID OF X(8) (-0.6122, -0.5999) A B C X1638 X2 X9 X654 X918 X210 X926 X11 X1146 X1639 (a, b, c) = (5, 6, 7) | AB = 1

X1639 (TRIPOLAR CENTROID OF X8) 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 \(f(a,b,c) = bc(b - c)(b + c - a)(b + c - 2a)\) (M. Iliev, 5/13/07)
Search Value (6, 9, 13): \(10.016643019005\)
▸ Incident Central Lines5 lines

{2, 918}, {9, 654}, {11, 1146}, {210, 926}, {522, 650}

▸ Functional Relations2 relations

  • X1639 = reflection of X1638 in X2

  • X1639 = centroid of (degenerate) side-triangle of ABC and Gemini triangle 15