X3500

INTERSECTION OF LINES X1X_295 AND X3X_238

X3500 = trilinear pole of line X659X1459
< 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, 238 }: Central Line L(3, 238) { 63, 194 }: Central Line L(63, 194) { 1, 295 }: Central Line L(1, 295) { 222, 1424 }: Central Line L(222, 1424) { 384, 3501 }: Central Line L(384, 3501) { 3492, 3502 }: Central Line L(3492, 3502) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3501 = INTERSECTION OF LINES X(1)X(39) AND X(4)X(9) (0.5467, 0.2440) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_238 = -LINE CONJUGATE OF X(37) (1.6190, 1.4775) X_63 = ISOGONAL CONJUGATE OF X(19) (0.4566, 0.0823) X_194 = -CEVA CONJUGATE OF X(2) (0.6989, 0.3222) X_1 = INCENTER (0.5714, 0.2333) X_295 = ISOGONAL CONJUGATE OF X(242) (1.0582, 0.0142) X_222 = -CEVA CONJUGATE OF X(56) (0.5653, 0.1568) X_1424 = -BETH CONJUGATE OF X(194) (0.6912, 0.4122) X_384 = THE CONWAY POINT: EULER LINE INTERCEPT OF LINE X(32)X(76) (0.5532, 0.2412) X_3492 = INTERSECTION OF LINES X(4)X(83) AND X(32)X(695) (0.5108, 0.0518) X_3502 = ISOGONAL CONJUGATE OF X(3494) (0.6508, 0.3268) X_3500 = INTERSECTION OF LINES X(1)X(295) AND X(3)X(238) (0.5973, 0.2216) A B C X3501 X3 X238 X63 X194 X1 X295 X222 X1424 X384 X3492 X3502 X3500 (a, b, c) = (5, 6, 7) | AB = 1

X3500 (INTERSECTION OF LINES X1X_295 AND X3X_238) 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 \(f(a,b,c) = 1/[a^{2}b + a^{2}c - a(b^{2} + bc + c^{2}) + bc( b + c)] (E\). Danneels)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(1.138038753155\)

X3500 lies on the cubic Z(X384).

▸ Incident Central Lines6 lines

{1, 295}, {3, 238}, {63, 194}, {222, 1424}, {384, 3501}, {3492, 3502}

▸ Functional Relations4 relations