X3220

INTERSECTION OF LINES X3X_9 AND X36X_238

X3220 = crosspoint of X58 and X103
< 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, 9 }: Central Line L(3, 9) { 25, 57 }: Central Line L(25, 57) { 22, 63 }: Central Line L(22, 63) { 1, 159 }: Central Line L(1, 159) { 36, 238 }: Central Line L(36, 238) { 56, 269 }: Central Line L(56, 269) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_58 = ISOGONAL CONJUGATE OF X(10) (0.6107, 0.2850) X_103 = ANTIPODE OF X(101) (0.7857, -0.3208) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_9 = MITTENPUNKT (0.5110, 0.1615) X_25 = HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES (0.6329, 0.4497) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_22 = EXETER POINT (0.4143, -0.1221) X_63 = ISOGONAL CONJUGATE OF X(19) (0.4566, 0.0823) X_1 = INCENTER (0.5714, 0.2333) X_159 = -OF-TANGENTIAL-TRIANGLE (0.4211, -0.7266) X_36 = INVERSE-IN-CIRCUMCIRCLE OF INCENTER (1.3333, 1.6330) X_238 = -LINE CONJUGATE OF X(37) (1.6190, 1.4775) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_269 = ISOGONAL CONJUGATE OF X(200) (0.6369, 0.3847) X_3220 = INTERSECTION OF LINES X(3)X(9) AND X(36)X(238) (0.8333, 1.9052) A B C X58 X103 X3 X9 X25 X57 X22 X63 X1 X159 X36 X238 X56 X269 X3220 (a, b, c) = (5, 6, 7) | AB = 1

X3220 (INTERSECTION OF LINES X3X_9 AND X36X_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 \(f(a,b,c) = a[a^{4} - b^{4} - c^{4} + bc(b^{2} + c^{2} - a^{2})]\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-1.555329245544\)
▸ Incident Central Lines22 lines

{1, 159}, {3, 9}, {19, 990}, {22, 63}, {25, 57}, {35, 984}, {36, 238}, {48, 991}, {56, 269}, {58, 1474}, {100, 2751}, {101, 1818}, {103, 2272}, {104, 2728}, {154, 222}, {165, 197}, {184, 2003}, {219, 1350}, {511, 2323}, {603, 2212}, {759, 2722}, {1040, 1763}

▸ Functional Relations3 relations

Notes

X3220 is the homothetic center of the following two triangles: tangential triangles of the excentral triangle, and excentral triangle of the tangential triangle. (Note from Peter Moses, 1/24/2007)