X3010

(LEMOINE AXIS)∩(SODDY LINE)

< 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, 7 }: Soddy Line { 187, 237 }: Central Line L(187, 237) { 31, 1951 }: Central Line L(31, 1951) 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_7 = GERGONNE POINT (0.5903, 0.2769) X_187 = INVERSE-IN-CIRCUMCIRCLE OF X(6) (SCHOUTE CENTER) (1.1986, 1.2559) X_237 = -LINE CONJUGATE OF X(2) (0.9894, 1.3825) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_1951 = CROSSDIFFERENCE OF PU(20) (3.2396, 6.6676) X_3010 = (LEMOINE AXIS)∩(SODDY LINE) (1.0519, 1.3447) A B C X1 X7 X187 X237 X31 X1951 X3010 (a, b, c) = (5, 6, 7) | AB = 1

X3010 ((LEMOINE AXIS)∩(SODDY LINE)) 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 \(f(a,b,c) = ab[\sec^{2}(A/2) - \sec^{2}(C/2)] + ac[\sec^{2}(A/2) - \sec^{2}(B/2)]\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-1.533329950602\)
▸ Incident Central Lines3 lines

{1, 7}, {31, 1951}, {187, 237}