X1569

MOSES-CIRCLE ANTIPODE OF X115

X1569 is the moses-circle antipode of X115.
< 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) { 99, 194 }: Central Line L(99, 194) { 5, 39 }: Central Line L(5, 39) { 32, 99 }: Central Line L(32, 99) { 98, 574 }: Central Line L(98, 574) { 76, 620 }: Central Line L(76, 620) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_99 = STEINER POINT (0.1109, 0.4322) X_194 = -CEVA CONJUGATE OF X(2) (0.6989, 0.3222) X_5 = NINE-POINT CENTER (0.5561, 0.2489) X_39 = BROCARD MIDPOINT (0.5778, 0.2305) X_32 = 3rd POWER POINT (0.6400, 0.3332) X_98 = TARRY POINT (0.8891, -0.2281) X_574 = HARMONIC OF X(187) (0.5539, 0.1910) X_76 = 3rd BROCARD POINT (0.4567, 0.1388) X_620 = MIDPOINT OF X(618) AND X(619) (0.4308, 0.2580) X_1569 = MOSES-CIRCLE ANTIPODE OF X(115) (0.4049, 0.3772) A B C X99 X194 X5 X39 X32 X98 X574 X76 X620 X1569 (a, b, c) = (5, 6, 7) | AB = 1

X1569 (MOSES-CIRCLE ANTIPODE OF X115) 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 \(f(a,b,c) = bc[2a^{2}(b^{2} + c^{2})(1 - 4 \sin^{2}\omega ) - (b^{2} - c^{2})^{2}]\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(0.904270831017\)
▸ Incident Central Lines5 lines

{5, 39}, {32, 99}, {76, 620}, {98, 574}, {543, 598}

▸ Functional Relations3 relations