X3359

MIDPOINT OF X2096 AND X3421

X3359 is the midpoint of X2096 and X3421.
< 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) { 2096, 3421 }: Central Line L(2096, 3421) { 1, 3 }: OI Line (Incenter–Circumcenter Line) { 9, 119 }: Central Line L(9, 119) { 84, 355 }: Central Line L(84, 355) { 200, 912 }: Central Line L(200, 912) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2096 = REFLECTION OF X(4) IN X(57) (0.6153, 0.2263) X_3421 = ISOGONAL CONJUGATE OF X(3420) (0.4271, 0.0555) X_1 = INCENTER (0.5714, 0.2333) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_9 = MITTENPUNKT (0.5110, 0.1615) X_119 = FEUERBACH ANTIPODE (0.3776, 0.4312) X_84 = ISOGONAL CONJUGATE OF X(40) (0.6071, 0.6816) X_355 = FUHRMANN CENTER (0.5408, 0.2645) X_200 = -CEVA CONJUGATE OF X(9) (0.4392, 0.1037) X_912 = -CEVA CONJUGATE OF X(3) (0.0031, -0.0428) X_3359 = MIDPOINT OF X(2096) AND X(3421) (0.5212, 0.1409) A B C X2096 X3421 X1 X3 X9 X119 X84 X355 X200 X912 X3359 (a, b, c) = (5, 6, 7) | AB = 1

X3359 (MIDPOINT OF X2096 AND X3421) 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 \(f(a,b,c) = (a - b + c)(a + b - c)(a + b + c) + kabc\), where \(k = -2(2R - r)/(R - r)\). (Peter Moses, January 11, 2011)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(6.127436285227\)
▸ Incident Central Lines13 lines

{1, 3}, {2, 1519}, {9, 119}, {10, 1158}, {63, 2096}, {72, 2057}, {84, 355}, {200, 912}, {997, 2800}, {1103, 3157}, {1452, 1753}, {1722, 3073}, {2550, 3358}

▸ Functional Relations2 relations