X1788

MIMOSA TRANSFORM OF X1476

X1788 = cevapoint of X46 and X1722
< 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) { 7, 12 }: Central Line L(7, 12) { 4, 46 }: Central Line L(4, 46) { 8, 56 }: Central Line L(8, 56) { 2, 65 }: Central Line L(2, 65) { 10, 57 }: Central Line L(10, 57) { 43, 73 }: Central Line L(43, 73) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_46 = -CEVA CONJUGATE OF X(1) (0.6917, 0.4543) X_1722 = MIMOSA TRANSFORM OF X(56) (0.8571, 0.5132) X_7 = GERGONNE POINT (0.5903, 0.2769) X_12 = {X(1),X(5)}-HARMONIC CONJUGATE OF X(11) (0.5641, 0.2407) X_4 = ORTHOCENTER (0.6122, 0.3958) X_8 = NAGEL POINT (0.4694, 0.1333) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_2 = CENTROID (0.5374, 0.2000) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_43 = -CEVA CONJUGATE OF X(1) (0.6358, 0.2963) X_73 = CROSSPOINT OF INCENTER AND CIRCUMCENTER (0.5487, 0.1428) X_1788 = MIMOSA TRANSFORM OF X(1476) (0.6161, 0.4547) A B C X46 X1722 X7 X12 X4 X8 X56 X2 X65 X10 X57 X43 X73 X1788 (a, b, c) = (5, 6, 7) | AB = 1

X1788 (MIMOSA TRANSFORM OF X1476) 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 \(f(a,b,c) = - (\cos A)/x + (\cos B)/y + (\cos C)/z\),\(x : y : z\) = X1476
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-0.560997052201\)
▸ Incident Central Lines42 lines

{1, 631}, {2, 65}, {4, 46}, {7, 12}, {8, 56}, {10, 57}, {11, 962}, {20, 1155}, {34, 1722}, {36, 944}, {40, 497}, {43, 73}, {55, 938}, {109, 1724}, {145, 1319}, {165, 950}, {171, 1451}, {200, 1467}, {201, 986}, {208, 1861}, {225, 1738}, {226, 1698}, {227, 241}, {278, 1714}, {281, 579}, {329, 1329}, {344, 1284}, {345, 1403}, {377, 1454}, {387, 1214}, {412, 1857}, {484, 1479}, {519, 1420}, {580, 1771}, {651, 1406}, {653, 1118}, {899, 1042}, {958, 1466}, {961, 1150}, {978, 1457}, {1068, 1772}, {1707, 1877}

▸ Functional Relations2 relations