X1570

MOSES-CIRCLE INVERSE OF X3

X1570 is the moses-circle inverse of X3.
< 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) { 3, 6 }: Brocard Axis { 193, 625 }: Central Line L(193, 625) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_193 = -CEVA CONJUGATE OF X(2) (0.7878, 0.4690) X_625 = MIDPOINT OF X(623) AND X(624) (0.2068, -0.3280) X_1570 = MOSES-CIRCLE INVERSE OF X(3) (0.4005, -0.0623) A B C X3 X6 X193 X625 X1570 (a, b, c) = (5, 6, 7) | AB = 1

X1570 (MOSES-CIRCLE INVERSE OF X3) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(a(\cot A + \cot \omega - 4 \tan \omega ) : :\)
Search Value (6, 9, 13): \(1.937505905952\)
▸ Alternate Coordinates1 form

  • Trilinears: \(a(2a^{4} + 3b^{4} + 3c^{4} - 2b^{2}c^{2} -3a^{2}b^{2} - 3a^{2}c^{2}) : :\)

▸ Incident Central Lines2 lines

{3, 6}, {193, 625}

▸ Functional Relations7 relations