X3501

INTERSECTION OF LINES X1X_39 AND X4X_9

X3501 = crosssum of X649 and X3123
< 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) { 4, 9 }: Orthocenter–Spieker Line { 1, 39 }: Central Line L(1, 39) { 41, 100 }: Central Line L(41, 100) { 43, 213 }: Central Line L(43, 213) { 57, 345 }: Central Line L(57, 345) { 8, 672 }: Central Line L(8, 672) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3500 = INTERSECTION OF LINES X(1)X(295) AND X(3)X(238) (0.5973, 0.2216) X_4 = ORTHOCENTER (0.6122, 0.3958) X_9 = MITTENPUNKT (0.5110, 0.1615) X_1 = INCENTER (0.5714, 0.2333) X_39 = BROCARD MIDPOINT (0.5778, 0.2305) X_41 = -CEVA CONJUGATE OF X(31) (0.5823, 0.2244) X_100 = ANTICOMPLEMENT OF FEUERBACH POINT (0.1429, 0.4666) X_43 = -CEVA CONJUGATE OF X(1) (0.6358, 0.2963) X_213 = -CEVA CONJUGATE OF X(42) (0.6135, 0.2833) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_345 = ISOTOMIC CONJUGATE OF X(278) (0.3405, 0.0381) X_8 = NAGEL POINT (0.4694, 0.1333) X_672 = CROSSDIFFERENCE OF X(1) AND X(514) (1.9245, 2.2184) X_3501 = INTERSECTION OF LINES X(1)X(39) AND X(4)X(9) (0.5467, 0.2440) A B C X3500 X4 X9 X1 X39 X41 X100 X43 X213 X57 X345 X8 X672 X3501 (a, b, c) = (5, 6, 7) | AB = 1

X3501 (INTERSECTION OF LINES X1X_39 AND X4X_9) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \((a - b) (a - c) (b + c) + a b c : :\)
Search Value (6, 9, 13): \(2.132316726282\)

X3501 lies on the cubic Z(X384).

▸ Incident Central Lines22 lines

{1, 39}, {2, 1334}, {3, 2329}, {4, 9}, {7, 979}, {8, 672}, {32, 3494}, {37, 986}, {41, 100}, {43, 213}, {57, 345}, {63, 2896}, {76, 1423}, {145, 1475}, {220, 1376}, {321, 2198}, {346, 1400}, {384, 3500}, {404, 644}, {484, 1759}, {579, 2321}, {1575, 2176}

▸ Functional Relations4 relations