X1718

MIMOSA TRANSFORM OF X36

< 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, 5 }: Feuerbach Line { 34, 46 }: Central Line L(34, 46) { 106, 614 }: Central Line L(106, 614) { 36, 1455 }: Central Line L(36, 1455) { 244, 1468 }: Central Line L(244, 1468) { 4, 1717 }: Central Line L(4, 1717) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1 = INCENTER (0.5714, 0.2333) X_5 = NINE-POINT CENTER (0.5561, 0.2489) X_34 = -BETH CONJUGATE OF X(4) (0.6332, 0.4792) X_46 = -CEVA CONJUGATE OF X(1) (0.6917, 0.4543) X_106 = Λ(INCENTER, CENTROID) (1.0000, 0.0000) X_614 = INTERSECTION OF LINES X(1)X(2) AND X(11)X(33) (0.6310, 0.2916) X_36 = INVERSE-IN-CIRCUMCIRCLE OF INCENTER (1.3333, 1.6330) X_1455 = -BETH CONJUGATE OF X(515) (0.6407, 1.1028) X_244 = -LINE CONJUGATE OF X(100) (0.7857, 0.1166) X_1468 = -BETH CONJUGATE OF X(958) (0.6033, 0.2751) X_4 = ORTHOCENTER (0.6122, 0.3958) X_1717 = MIMOSA TRANSFORM OF X(35) (0.6295, 0.3852) X_1718 = MIMOSA TRANSFORM OF X(36) (0.1143, 0.6999) A B C X1 X5 X34 X46 X106 X614 X36 X1455 X244 X1468 X4 X1717 X1718 (a, b, c) = (5, 6, 7) | AB = 1

X1718 (MIMOSA TRANSFORM OF X36) 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 \(f(a,b,c) = - (\cos A)/x + (\cos B)/y + (\cos C)/z\),\(x : y : z\) = X36
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(0.733492846524\)
▸ Incident Central Lines11 lines

{1, 5}, {4, 1717}, {6, 1781}, {34, 46}, {36, 1455}, {90, 1720}, {106, 614}, {244, 1468}, {1723, 1783}, {1727, 1735}, {1737, 1870}

▸ Functional Relations2 relations