X1908

MIDPOINT OF PU(8)

X1908 is the midpoint of pu(8).
< 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) { 171, 292 }: Central Line L(171, 292) { 42, 649 }: Central Line L(42, 649) { 39, 1155 }: Central Line L(39, 1155) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_171 = {X(2), X(31)}-HARMONIC CONJUGATE OF X(238) (0.5819, 0.2525) X_292 = -HIRST INVERSE OF X(291) (1.0127, 0.0417) X_42 = CROSSPOINT OF INCENTER AND SYMMEDIAN POINT (0.5880, 0.2495) X_649 = CROSSDIFFERENCE OF X(1) and X(2) (-21.0000, 14.6969) X_39 = BROCARD MIDPOINT (0.5778, 0.2305) X_1155 = SCHRÖDER POINT (1.7143, 2.3328) X_1908 = MIDPOINT OF PU(8) (0.5880, 0.2495) A B C X171 X292 X42 X649 X39 X1155 X1908 (a, b, c) = (5, 6, 7) | AB = 1

X1908 (MIDPOINT OF PU(8)) 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 \(f(a,b,c) = a^{2}(b^{3} + c^{3}) + 2abc(a^{2} + bc)\) (Wimalasiri Perera, August 29, 2011)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(1.280235976089\)
▸ Incident Central Lines6 lines

{39, 1155}, {42, 649}, {43, 2235}, {171, 292}, {551, 2666}, {2243, 2276}