X1798

INVERSE MIMOSA TRANSFORM OF X58

X1798 = cevapoint of X3 and X1437
< 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, 60 }: Central Line L(6, 60) { 65, 81 }: Central Line L(65, 81) { 71, 283 }: Central Line L(71, 283) { 54, 970 }: Central Line L(54, 970) { 110, 960 }: Central Line L(110, 960) { 58, 1245 }: Central Line L(58, 1245) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_1437 = -BETH CONJUGATE OF X(283) (0.5584, 0.1373) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_60 = ISOGONAL CONJUGATE OF X(12) (0.5790, 0.2258) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_81 = CEVAPOINT OF INCENTER AND SYMMEDIAN POINT (0.5849, 0.2510) X_71 = ISOGONAL CONJUGATE OF X(27) (0.4807, 0.0915) X_283 = -CROSS CONJUGATE OF X(21) (0.4475, 0.0704) X_54 = KOSNITA POINT (0.5880, 0.2176) X_970 = CENTER OF THE APOLLONIUS CIRCLE (0.2643, -0.2872) X_110 = FOCUS OF KIEPERT PARABOLA (0.2516, 0.5478) X_960 = INTERSECTION OF LINES X(1)X(6) AND X(5)X(10) (0.5041, 0.1533) X_58 = ISOGONAL CONJUGATE OF X(10) (0.6107, 0.2850) X_1245 = ISOGONAL CONJUGATE OF X(1010) (0.5991, 0.2625) X_1798 = INVERSE MIMOSA TRANSFORM OF X(58) (0.5254, 0.1199) A B C X3 X1437 X6 X60 X65 X81 X71 X283 X54 X970 X110 X960 X58 X1245 X1798 (a, b, c) = (5, 6, 7) | AB = 1

X1798 (INVERSE MIMOSA TRANSFORM OF X58) 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 \(f(a,b,c) = (\cos A)/(y + z)\),\(x : y : z\) = X58
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(16.254593549071\)
▸ Incident Central Lines9 lines

{6, 60}, {54, 970}, {58, 1245}, {65, 81}, {71, 283}, {72, 1437}, {73, 1790}, {110, 960}, {285, 1903}

▸ Functional Relations2 relations