X2112

POINT KEPLER IV

X2112 = X238-Ceva conjugate of X31
< 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, 41 }: Central Line L(1, 41) { 31, 292 }: Central Line L(31, 292) { 604, 651 }: Central Line L(604, 651) { 172, 1201 }: Central Line L(172, 1201) { 6, 2054 }: Central Line L(6, 2054) { 1015, 1468 }: Central Line L(1015, 1468) 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_41 = -CEVA CONJUGATE OF X(31) (0.5823, 0.2244) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_292 = -HIRST INVERSE OF X(291) (1.0127, 0.0417) X_604 = -CEVA CONJUGATE OF X(31) (0.6442, 0.3744) X_651 = TRILINEAR POLE OF LINE X(1)X(3) (0.3048, 0.5599) X_172 = TRILINEAR PRODUCT X(6)*X(171) (0.6080, 0.2866) X_1201 = 3rd SARAGOSSA POINT OF X(56) (0.6184, 0.2793) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_2054 = -ISOCONJUGATE OF X(1931) (0.9934, -0.0217) X_1015 = EXSIMILICENTER OF MOSES CIRCLE AND INCIRCLE (0.7982, 0.1348) X_1468 = -BETH CONJUGATE OF X(958) (0.6033, 0.2751) X_2112 = POINT KEPLER IV (-0.0981, 0.7800) A B C X1 X41 X31 X292 X604 X651 X172 X1201 X6 X2054 X1015 X1468 X2112 (a, b, c) = (5, 6, 7) | AB = 1

X2112 (POINT KEPLER IV) 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 \(f(a,b,c) = a[a^{4} - bca^{2} - (b^{3} + c^{3})a + 2b^{2}c^{2}]\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(1.161252599580\)
▸ Incident Central Lines10 lines

{1, 41}, {6, 2054}, {31, 292}, {172, 1201}, {238, 2113}, {604, 651}, {672, 2115}, {1015, 1468}, {1914, 2109}, {2106, 2111}

▸ Functional Relations5 relations