X2108

POINT KEPLER I

X2108 = perspector of 2nd Sharygin triangle and unary cofactor triangle of 1st Sharygin triangle
< 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, 39 }: Central Line L(1, 39) { 31, 43 }: Central Line L(31, 43) { 170, 411 }: Central Line L(170, 411) { 2, 846 }: Central Line L(2, 846) { 42, 1051 }: Central Line L(42, 1051) { 238, 1575 }: Central Line L(238, 1575) 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_39 = BROCARD MIDPOINT (0.5778, 0.2305) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_43 = -CEVA CONJUGATE OF X(1) (0.6358, 0.2963) X_170 = -ALEPH CONJUGATE OF X(9) (0.4465, -0.0557) X_411 = EULER X(21)-2nd-SUBSTITUTION POINT (0.4414, -0.0514) X_2 = CENTROID (0.5374, 0.2000) X_846 = 4th SHARYGIN POINT (0.5437, 0.1969) X_42 = CROSSPOINT OF INCENTER AND SYMMEDIAN POINT (0.5880, 0.2495) X_1051 = POINT ALGORAB (0.5863, 0.2501) X_238 = -LINE CONJUGATE OF X(37) (1.6190, 1.4775) X_1575 = EXSIMILICENTER OF SPIEKER AND (1/2)-MOSES CIRCLES (2.5675, 1.8684) X_2108 = POINT KEPLER I (-0.3883, 0.6500) A B C X1 X39 X31 X43 X170 X411 X2 X846 X42 X1051 X238 X1575 X2108 (a, b, c) = (5, 6, 7) | AB = 1

X2108 (POINT KEPLER I) 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 \(f(a,b,c) = (b + c)a^{3} - (b^{2} - bc + c^{2})a^{2} - (b + c)(b^{2} + c^{2})a + bc(b^{2} + bc + c^{2})\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(5.319073774755\)
▸ Incident Central Lines9 lines

{1, 39}, {2, 846}, {3, 2053}, {31, 43}, {42, 1051}, {170, 411}, {238, 1575}, {672, 1282}, {1011, 1283}

▸ Functional Relations3 relations