X3313

INTERSECTION OF LINES X3X_6 AND X66X_69

X3313 = X69-Ceva conjugate of X141
< 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) { 3, 6 }: Brocard Axis { 66, 69 }: Central Line L(66, 69) { 22, 206 }: Central Line L(22, 206) { 159, 394 }: Central Line L(159, 394) { 141, 427 }: Central Line L(141, 427) { 1216, 1352 }: Central Line L(1216, 1352) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_66 = ISOGONAL CONJUGATE OF X(22) (0.5912, 1.0593) X_69 = SYMMEDIAN POINT OF THE ANTICOMPLEMENTARY TRIANGLE (0.4122, 0.0654) X_22 = EXETER POINT (0.4143, -0.1221) X_206 = -CEVA CONJUGATE OF X(32) (0.5105, -0.2297) X_159 = -OF-TANGENTIAL-TRIANGLE (0.4211, -0.7266) X_394 = -CEVA CONJUGATE OF X(3) (0.3778, 0.0284) X_141 = COMPLEMENT OF SYMMEDIAN POINT (0.5061, 0.1663) X_427 = COMPLEMENT OF X(22) (0.5990, 0.3610) X_1216 = ISOGONAL CONJUGATE OF X(1179) (0.4484, 0.0709) X_1352 = REFLECTION OF X(6) IN X(5) (0.5122, 0.2306) X_3313 = INTERSECTION OF LINES X(3)X(6) AND X(66)X(69) (0.3845, -0.0887) A B C X3 X6 X66 X69 X22 X206 X159 X394 X141 X427 X1216 X1352 X3313 (a, b, c) = (5, 6, 7) | AB = 1

X3313 (INTERSECTION OF LINES X3X_6 AND X66X_69) 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 \(f(a,b,c) = a(b^{2} + c^{2})(b^{4} + c^{4} - a^{4})\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(8.519138124409\)
▸ Incident Central Lines7 lines

{3, 6}, {22, 206}, {66, 69}, {141, 427}, {159, 394}, {1205, 2854}, {1216, 1352}

▸ Functional Relations5 relations