X3485

INTERSECTION OF LINES X1X_4 AND X7X_21

X3485 = X968-cross conjugate of X966
< 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, 4 }: Incenter–Orthocenter Line { 8, 12 }: Central Line L(8, 12) { 7, 21 }: Central Line L(7, 21) { 2, 65 }: Central Line L(2, 65) { 85, 350 }: Central Line L(85, 350) { 55, 411 }: Central Line L(55, 411) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_968 = POINT ALDERAMIN (0.5557, 0.2126) X_966 = INTERSECTION OF LINES X(2)X(6) AND X(4)X(9) (0.5191, 0.1803) X_1 = INCENTER (0.5714, 0.2333) X_4 = ORTHOCENTER (0.6122, 0.3958) X_8 = NAGEL POINT (0.4694, 0.1333) X_12 = {X(1),X(5)}-HARMONIC CONJUGATE OF X(11) (0.5641, 0.2407) X_7 = GERGONNE POINT (0.5903, 0.2769) X_21 = SCHIFFLER POINT (0.5287, 0.1771) X_2 = CENTROID (0.5374, 0.2000) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_85 = ISOTOMIC CONJUGATE OF X(9) (0.5610, 0.2421) X_350 = -HIRST INVERSE OF X(75) (-3.5227, -3.1370) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_411 = EULER X(21)-2nd-SUBSTITUTION POINT (0.4414, -0.0514) X_3485 = INTERSECTION OF LINES X(1)X(4) AND X(7)X(21) (0.5770, 0.2553) A B C X968 X966 X1 X4 X8 X12 X7 X21 X2 X65 X85 X350 X55 X411 X3485 (a, b, c) = (5, 6, 7) | AB = 1

X3485 (INTERSECTION OF LINES X1X_4 AND X7X_21) 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 \(f(A,B,C) = \cos A + \cos B + \cos C + \cos B \cos C\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(1.064667072482\)
▸ Incident Central Lines31 lines

{1, 4}, {2, 65}, {7, 21}, {8, 12}, {11, 938}, {20, 1836}, {29, 1118}, {46, 631}, {55, 411}, {57, 1125}, {78, 2550}, {85, 350}, {196, 1940}, {221, 940}, {238, 1451}, {277, 2140}, {329, 958}, {354, 1858}, {376, 1770}, {443, 997}, {459, 1482}, {551, 1420}, {608, 2303}, {908, 2551}, {945, 1065}, {986, 1393}, {1038, 2263}, {1159, 1656}, {1468, 1935}, {1854, 2883}, {2171, 2345}

▸ Functional Relations1 relation