X2887

COMPLEMENTARY CONJUGATE OF X37

X2887 = complement of X31
< 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) { 10, 12 }: Central Line L(10, 12) { 2, 31 }: Central Line L(2, 31) { 120, 124 }: Central Line L(120, 124) { 39, 734 }: Central Line L(39, 734) { 37, 744 }: Central Line L(37, 744) { 141, 674 }: Central Line L(141, 674) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_12 = {X(1),X(5)}-HARMONIC CONJUGATE OF X(11) (0.5641, 0.2407) X_2 = CENTROID (0.5374, 0.2000) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_120 = -OF-MEDIAL-TRIANGLE (0.3204, 0.3466) X_124 = -OF-MEDIAL-TRIANGLE (0.6243, 0.0030) X_39 = BROCARD MIDPOINT (0.5778, 0.2305) X_734 = EVEN (- 2, 3) INFINITY POINT (0.1172, -0.2097) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_744 = EVEN (- 1, 3) INFINITY POINT (0.1365, -0.2286) X_141 = COMPLEMENT OF SYMMEDIAN POINT (0.5061, 0.1663) X_674 = CROSSDIFFERENCE OF X(6) AND X(514) (0.2078, -0.2856) X_2887 = COMPLEMENTARY CONJUGATE OF X(37) (0.4947, 0.1495) A B C X10 X12 X2 X31 X120 X124 X39 X734 X37 X744 X141 X674 X2887 (a, b, c) = (5, 6, 7) | AB = 1

X2887 (COMPLEMENTARY CONJUGATE OF X37) 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 \(f(a,b,c) = bc(b + c)(b^{2} + c^{2} - bc)\) (M. Iliev, 5/13/07)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(3.672915222862\)
▸ Incident Central Lines13 lines

{1, 977}, {2, 31}, {10, 12}, {37, 744}, {39, 734}, {120, 124}, {141, 674}, {306, 740}, {334, 1581}, {626, 766}, {1111, 1233}, {1329, 2390}, {2205, 2240}

▸ Functional Relations13 relations