X1723

MIMOSA TRANSFORM OF X57

X1723 = crosspoint of X653 and X765
< 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 { 19, 46 }: Central Line L(19, 46) { 35, 380 }: Central Line L(35, 380) { 36, 610 }: Central Line L(36, 610) { 90, 1172 }: Central Line L(90, 1172) { 169, 1400 }: Central Line L(169, 1400) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_653 = TRILINEAR POLE OF LINE X(1)X(4) (0.5097, 0.6030) X_765 = CEVAPOINT OF X(1) AND X(100) (0.4286, 0.3110) X_1 = INCENTER (0.5714, 0.2333) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_19 = CLAWSON POINT (0.6246, 0.4244) X_46 = -CEVA CONJUGATE OF X(1) (0.6917, 0.4543) X_35 = {X(1),X(3)}-HARMONIC CONJUGATE OF X(36) (0.5373, 0.1706) X_380 = INTERSECTION OF LINES X(1)X(19) AND X(9)X(55) (0.5631, 0.2035) X_36 = INVERSE-IN-CIRCUMCIRCLE OF INCENTER (1.3333, 1.6330) X_610 = -CEVA CONJUGATE OF X(1) (0.4310, -0.2713) X_90 = -CROSS CONJUGATE OF X(1) (0.1022, 0.0201) X_1172 = 1st SARAGOSSA POINT OF X(48) (0.6100, 0.3717) X_169 = -CEVA CONJUGATE OF X(1) (0.5497, 0.2510) X_1400 = -BETH CONJUGATE OF X(37) (0.6246, 0.3268) X_1723 = MIMOSA TRANSFORM OF X(57) (0.7970, 0.5012) A B C X653 X765 X1 X6 X19 X46 X35 X380 X36 X610 X90 X1172 X169 X1400 X1723 (a, b, c) = (5, 6, 7) | AB = 1

X1723 (MIMOSA TRANSFORM OF X57) 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 \(f(a,b,c) = - (\cos A)/x + (\cos B)/y + (\cos C)/z\),\(x : y : z\) = X57
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-1.161152331835\)
▸ Incident Central Lines16 lines

{1, 6}, {19, 46}, {35, 380}, {36, 610}, {57, 1762}, {90, 1172}, {169, 1400}, {278, 1708}, {281, 1737}, {672, 1766}, {920, 1249}, {928, 1047}, {1707, 1709}, {1718, 1783}, {1722, 1880}, {1729, 1744}

▸ Functional Relations4 relations