X2106

POINT KEPLER I

X2106 = X2664-cross conjugate of X2669
< 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) { 2, 6 }: Centroid–Symmedian Line { 105, 805 }: Central Line L(105, 805) { 238, 741 }: Central Line L(238, 741) { 213, 1509 }: Central Line L(213, 1509) { 873, 894 }: Central Line L(873, 894) { 292, 1931 }: Central Line L(292, 1931) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2664 = CROSSDIFFERENCE OF PU(84) (1.9947, 1.6278) X_2669 = CROSSDIFFERENCE OF PU(85) (3.1271, 2.5227) X_2 = CENTROID (0.5374, 0.2000) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_105 = Λ(INCENTER, SYMMEDIAN POINT) (0.9714, -0.0933) X_805 = o-(- 2, 2) CIRCUMCIRCLE POINT (0.9729, -0.0897) X_238 = -LINE CONJUGATE OF X(37) (1.6190, 1.4775) X_741 = EVEN (- 1, 1) CIRCUMCIRCLE POINT (1.0071, 0.0451) X_213 = -CEVA CONJUGATE OF X(42) (0.6135, 0.2833) X_1509 = ISOGONAL CONJUGATE OF X(1500) (0.5682, 0.2347) X_873 = ISOGONAL CONJUGATE OF X(872) (0.5339, 0.2011) X_894 = ISOGONAL CONJUGATE OF X(893) (0.5501, 0.2184) X_292 = -HIRST INVERSE OF X(291) (1.0127, 0.0417) X_1931 = CROSSDIFFERENCE OF PU(32) (1.7418, 1.7715) X_2106 = POINT KEPLER I (1.5281, 1.2647) A B C X2664 X2669 X2 X6 X105 X805 X238 X741 X213 X1509 X873 X894 X292 X1931 X2106 (a, b, c) = (5, 6, 7) | AB = 1

X2106 (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 \(f(a,b,c) = (a + b)(a + c)(b^{2}c^{2} - a^{2}b^{2} - a^{2}c^{2} + abc(b + c - a))\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-3.198362755880\)
▸ Incident Central Lines10 lines

{2, 6}, {105, 805}, {213, 1509}, {238, 741}, {292, 1931}, {662, 1914}, {873, 894}, {1621, 1964}, {2111, 2112}, {2114, 2117}

▸ Functional Relations2 relations