X1108

CROSSPOINT OF X2 AND X84

X1108 is the midpoint of the bicentric pair \(y : z : x\) and \(z : x : y\), where \(x : y : z\) = X219
< A B C >: Reference Triangle △ABC < M_a M_b M_c >: Medial Triangle △M_a M_b M_c [ A B ]: Sideline AB (Base c = 1) [ B C ]: Sideline BC (Side a) [ C A ]: Sideline CA (Side b) { 2, 322 }: Central Line L(2, 322) { 1, 6 }: Incenter–Symmedian Line { 19, 56 }: Central Line L(19, 56) { 104, 112 }: Central Line L(104, 112) { 241, 347 }: Central Line L(241, 347) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) M_a = Midpoint M_a of BC (0.8061, 0.2999) M_b = Midpoint M_b of CA (0.3061, 0.2999) M_c = Midpoint M_c of AB (0.5000, 0.0000) X_2 = CENTROID (0.5374, 0.2000) X_322 = ISOTOMIC CONJUGATE OF X(84) (0.3430, -0.0168) 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_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_104 = ANTIPODE OF X(100) (0.8571, -0.2624) X_112 = Ψ(ORTHOCENTER, SYMMEDIAN POINT) (0.5162, 0.6121) X_241 = -LINE CONJUGATE OF X(55) (1.1217, 1.2442) X_347 = ISOTOMIC CONJUGATE OF X(280) (0.4531, -0.0404) X_1108 = CROSSPOINT OF X(2) AND X(84) (0.6346, 0.3084) A B C Ma Mb Mc X2 X322 X1 X6 X19 X56 X104 X112 X241 X347 X1108 (a, b, c) = (5, 6, 7) | AB = 1

X1108 (CROSSPOINT OF X2 AND X84) 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 \(f(a,b,c) = 2avw + cv^{2} + bw^{2} + u(bv + cw)\), where \(u : v : w\) = X219
Barycentrics: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where \(g(a,b,c) = af(a,b,c)\)
Search Value (6, 9, 13): \(0.721110910355\)
▸ Incident Central Lines7 lines

{1, 6}, {2, 322}, {19, 56}, {104, 112}, {241, 347}, {278, 393}, {517, 579}

▸ Functional Relations5 relations