X1713

MIMOSA TRANSFORM OF X27

X1713 = crosspoint of X765 and X823
< 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) { 1, 6 }: Incenter–Symmedian Line { 4, 579 }: Central Line L(4, 579) { 71, 950 }: Central Line L(71, 950) { 284, 1006 }: Central Line L(284, 1006) { 19, 1708 }: Central Line L(19, 1708) { 580, 1172 }: Central Line L(580, 1172) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_765 = CEVAPOINT OF X(1) AND X(100) (0.4286, 0.3110) X_823 = ISOGONAL CONJUGATE OF X(822) (0.5623, 0.6035) X_1 = INCENTER (0.5714, 0.2333) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_4 = ORTHOCENTER (0.6122, 0.3958) X_579 = HARMONIC OF X(284) (0.7212, 0.4674) X_71 = ISOGONAL CONJUGATE OF X(27) (0.4807, 0.0915) X_950 = CROSSPOINT OF X(8) AND X(29) (0.5621, 0.1961) X_284 = -CROSS CONJUGATE OF X(21) (0.5646, 0.2088) X_1006 = INTERCEPT OF EULER LINE AND LINEX(9)X(48) (0.5190, 0.1517) X_19 = CLAWSON POINT (0.6246, 0.4244) X_1708 = MIMOSA TRANSFORM OF X(7) (0.7332, 0.4848) X_580 = ORTHOGONAL OF X(284) (0.7089, 0.4470) X_1172 = 1st SARAGOSSA POINT OF X(48) (0.6100, 0.3717) X_1713 = MIMOSA TRANSFORM OF X(27) (0.8274, 0.5373) A B C X765 X823 X1 X6 X4 X579 X71 X950 X284 X1006 X19 X1708 X580 X1172 X1713 (a, b, c) = (5, 6, 7) | AB = 1

X1713 (MIMOSA TRANSFORM OF X27) 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 \(f(a,b,c) = - (\cos A)/x + (\cos B)/y + (\cos C)/z\),\(x : y : z\) = X27
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-0.327734789050\)
▸ Incident Central Lines10 lines

{1, 6}, {4, 579}, {19, 1708}, {71, 950}, {284, 1006}, {379, 1445}, {393, 1714}, {580, 1172}, {583, 1901}, {1712, 1741}

▸ Functional Relations3 relations