X910

CROSSPOINT OF X57 AND X105

X910 is the crosspoint of X57 and X105.
< 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) { 1530, 118 }: Central Line L(1530, 118) { 19, 25 }: Central Line L(19, 25) { 6, 57 }: Central Line L(6, 57) { 41, 65 }: Central Line L(41, 65) { 3, 169 }: Central Line L(3, 169) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1530 = ORTHOJOIN OF X(31) (-0.4898, -1.6288) X_118 = MIDPOINT OF X(4) AND X(101) (0.4133, 0.4603) X_19 = CLAWSON POINT (0.6246, 0.4244) X_25 = HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES (0.6329, 0.4497) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_41 = -CEVA CONJUGATE OF X(31) (0.5823, 0.2244) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_169 = -CEVA CONJUGATE OF X(1) (0.5497, 0.2510) X_910 = CROSSPOINT OF X(57) AND X(105) (1.3163, 2.5495) A B C X1530 X118 X19 X25 X6 X57 X41 X65 X3 X169 X910 (a, b, c) = (5, 6, 7) | AB = 1

X910 (CROSSPOINT OF X57 AND X105) 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 \(f(a,b,c) = a[wb^{2} + vc^{2} - a(wb + vc)]\),\(u : v : w\) = X3
Barycentrics: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where \(g(a,b,c) = af(a,b,c)\)
Search Value (6, 9, 13): \(-3.730955540803\)
▸ Incident Central Lines16 lines

{3, 169}, {6, 57}, {9, 165}, {19, 25}, {32, 1104}, {40, 220}, {41, 65}, {44, 513}, {46, 218}, {48, 354}, {101, 517}, {103, 971}, {105, 919}, {118, 516}, {227, 607}, {241, 294}

▸ Functional Relations8 relations