X3650

KS(EXTOUCH TRIANGLE)

< 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) { 8, 30 }: Central Line L(8, 30) { 9, 46 }: Central Line L(9, 46) { 21, 999 }: Central Line L(21, 999) { 553, 1125 }: Central Line L(553, 1125) { 758, 3057 }: Central Line L(758, 3057) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_8 = NAGEL POINT (0.4694, 0.1333) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_9 = MITTENPUNKT (0.5110, 0.1615) X_46 = -CEVA CONJUGATE OF X(1) (0.6917, 0.4543) X_21 = SCHIFFLER POINT (0.5287, 0.1771) X_999 = MIDPOINT OF X(1) AND X(57) (0.5926, 0.2722) X_553 = POINT MAIA II (0.5963, 0.2857) X_1125 = COMPLEMENT OF X(10) (0.5459, 0.2083) X_758 = EVEN (1, 3) INFINITY POINT (0.1821, -0.2671) X_3057 = INTERSECTION OF LINES X(1)X(3) AND X(10)X(11) (0.5388, 0.1733) X_3650 = KS(EXTOUCH TRIANGLE) (0.4301, 0.0304) A B C X8 X30 X9 X46 X21 X999 X553 X1125 X758 X3057 X3650 (a, b, c) = (5, 6, 7) | AB = 1

X3650 (KS(EXTOUCH TRIANGLE)) 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 \(f(a,b,c) = bc(2a + b + c)(-2a^{3} + b^{3} + c^{3} - a^{2}b - a^{2}c - b^{2}c - bc^{2} + 2ab^{2} + 2ac^{2} + 2abc)\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(6.972580663770\)
▸ Incident Central Lines5 lines

{8, 30}, {9, 46}, {21, 999}, {553, 1125}, {758, 3057}