X2030

RADICAL TRACE OF MOSES CIRCLE AND CIRCUMCIRCLE

X2030 = midpoint of X6 and X187
< 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) { 6, 187 }: Brocard Axis { 3, 6 }: Brocard Axis { 230, 542 }: Central Line L(230, 542) { 112, 843 }: Central Line L(112, 843) { 524, 620 }: Central Line L(524, 620) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_187 = INVERSE-IN-CIRCUMCIRCLE OF X(6) (SCHOUTE CENTER) (1.1986, 1.2559) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_230 = -CEVA CONJUGATE OF X(114) (0.9746, 0.6698) X_542 = DIRECTION OF VECTOR AX + BX + CX, where X = X(98) (0.1649, 0.6534) X_112 = Ψ(ORTHOCENTER, SYMMEDIAN POINT) (0.5162, 0.6121) X_843 = ISOGONAL CONJUGATE OF X(543) (0.1427, 0.4664) X_524 = ISOGONAL CONJUGATE OF X(111) (0.1376, -0.2297) X_620 = MIDPOINT OF X(618) AND X(619) (0.4308, 0.2580) X_2030 = RADICAL TRACE OF MOSES CIRCLE AND CIRCUMCIRCLE (0.8993, 0.7615) A B C X6 X187 X3 X230 X542 X112 X843 X524 X620 X2030 (a, b, c) = (5, 6, 7) | AB = 1

X2030 (RADICAL TRACE OF MOSES CIRCLE AND CIRCUMCIRCLE) 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 \(f(A,B,C) = \sin A - 4 \sin(A - 2\omega ) - \sin(A + 2\omega )\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(-0.423987621263\)
▸ Alternate Coordinates1 form

  • Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = a(4a^{4} + b^{4} + c^{4} - a^{2}b^{2} - a^{2}c^{2} - 4b^{2}c^{2})\) (M. Iliev, 5/13/07)

▸ Incident Central Lines5 lines

{3, 6}, {111, 1495}, {112, 843}, {230, 542}, {524, 620}

▸ Functional Relations2 relations