X2021

RADICAL TRACE OF GALLATLY CIRCLE AND CIRCUMCIRCLE

X2021 = midpoint of X39 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) { 39, 187 }: Brocard Axis { 3, 6 }: Brocard Axis { 620, 736 }: Central Line L(620, 736) { 115, 1513 }: Central Line L(115, 1513) { 538, 1569 }: Central Line L(538, 1569) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_39 = BROCARD MIDPOINT (0.5778, 0.2305) X_187 = INVERSE-IN-CIRCUMCIRCLE OF X(6) (SCHOUTE CENTER) (1.1986, 1.2559) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_620 = MIDPOINT OF X(618) AND X(619) (0.4308, 0.2580) X_736 = EVEN (- 2, 4) INFINITY POINT (0.9400, 0.6270) X_115 = CENTER OF KIEPERT HYPERBOLA (0.7507, 0.0838) X_1513 = ORTHOJOIN OF X(2) (1.0602, 1.5678) X_538 = DIRECTION OF VECTOR AX + BX + CX, where X = X(39) (1.0053, 0.5542) X_1569 = MOSES-CIRCLE ANTIPODE OF X(115) (0.4049, 0.3772) X_2021 = RADICAL TRACE OF GALLATLY CIRCLE AND CIRCUMCIRCLE (0.8882, 0.7432) A B C X39 X187 X3 X6 X620 X736 X115 X1513 X538 X1569 X2021 (a, b, c) = (5, 6, 7) | AB = 1

X2021 (RADICAL TRACE OF GALLATLY CIRCLE AND CIRCUMCIRCLE) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(3 \sin(A - \omega ) - 2 \sin(A + \omega ) + \sin(A + 3\omega ) : :\)
Search Value (6, 9, 13): \(-0.138202045565\)
▸ Alternate Coordinates1 form

  • Trilinears: \(a(b^{6} + c^{6} + 3a^{4}b^{2} + 3a^{4}c^{2} - 2a^{2}b^{4} - 2a^{2}c^{4} - 2a^{2}b^{2}c^{2} - b^{2}c^{4} - b^{4}c^{2}) : :\) (M. Iliev, 5/13/07)

▸ Incident Central Lines6 lines

{3, 6}, {30, 2025}, {115, 1513}, {538, 1569}, {620, 736}, {625, 1506}

▸ Functional Relations5 relations