X1778

MIMOSA TRANSFORM OF X1171

X1778 = cevapoint of X1707 and (1724)
< 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, 21 }: Central Line L(6, 21) { 9, 58 }: Central Line L(9, 58) { 37, 81 }: Central Line L(37, 81) { 28, 579 }: Central Line L(28, 579) { 90, 1172 }: Central Line L(90, 1172) { 44, 1333 }: Central Line L(44, 1333) 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_21 = SCHIFFLER POINT (0.5287, 0.1771) X_9 = MITTENPUNKT (0.5110, 0.1615) X_58 = ISOGONAL CONJUGATE OF X(10) (0.6107, 0.2850) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_81 = CEVAPOINT OF INCENTER AND SYMMEDIAN POINT (0.5849, 0.2510) X_28 = CEVAPOINT OF X(19) AND X(25) (0.6285, 0.4382) X_579 = HARMONIC OF X(284) (0.7212, 0.4674) X_90 = -CROSS CONJUGATE OF X(1) (0.1022, 0.0201) X_1172 = 1st SARAGOSSA POINT OF X(48) (0.6100, 0.3717) X_44 = -LINE CONJUGATE OF X(1) (2.1429, 2.0996) X_1333 = POINT ALULA (0.6308, 0.3181) X_1778 = MIMOSA TRANSFORM OF X(1171) (0.7708, 0.4831) A B C X6 X21 X9 X58 X37 X81 X28 X579 X90 X1172 X44 X1333 X1778 (a, b, c) = (5, 6, 7) | AB = 1

X1778 (MIMOSA TRANSFORM OF X1171) 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 \(f(a,b,c) = - (\cos A)/x + (\cos B)/y + (\cos C)/z\),\(x : y : z\) = X1171
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-1.473421561980\)
▸ Incident Central Lines13 lines

{6, 21}, {9, 58}, {19, 1707}, {28, 579}, {37, 81}, {44, 1333}, {90, 1172}, {284, 1743}, {580, 1765}, {896, 1761}, {966, 1010}, {1396, 1708}, {1474, 1732}

▸ Functional Relations1 relation