X3690

X1746com(EXTOUCH TRIANGLE)

X3690 = crosspoint of X71 and X72
< 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) { 9, 51 }: Central Line L(9, 51) { 25, 220 }: Central Line L(25, 220) { 37, 209 }: Central Line L(37, 209) { 42, 213 }: Central Line L(42, 213) { 71, 228 }: Central Line L(71, 228) { 101, 199 }: Central Line L(101, 199) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_71 = ISOGONAL CONJUGATE OF X(27) (0.4807, 0.0915) X_72 = ISOGONAL CONJUGATE OF X(28) (0.4367, 0.0733) X_9 = MITTENPUNKT (0.5110, 0.1615) X_51 = CENTROID OF ORTHIC TRIANGLE (0.6093, 0.3186) X_25 = HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES (0.6329, 0.4497) X_220 = -CEVA CONJUGATE OF X(55) (0.4826, 0.1278) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_209 = -CEVA CONJUGATE OF X(37) (0.7303, 0.4592) X_42 = CROSSPOINT OF INCENTER AND SYMMEDIAN POINT (0.5880, 0.2495) X_213 = -CEVA CONJUGATE OF X(42) (0.6135, 0.2833) X_228 = -CEVA CONJUGATE OF X(71) (0.5231, 0.1126) X_101 = Ψ(INCENTER, SYMMEDIAN POINT) (0.2143, 0.5249) X_199 = -CEVA CONJUGATE OF X(6) (0.4796, 0.0487) X_3690 = com(EXTOUCH TRIANGLE) (0.4611, 0.0818) A B C X71 X72 X9 X51 X25 X220 X37 X209 X42 X213 X228 X101 X199 X3690 (a, b, c) = (5, 6, 7) | AB = 1

X3690 (X1746com(EXTOUCH TRIANGLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Barycentrics: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = a^{2}(b + c)^{2}(- a^{2} + b^{2} + c^{2})\)
Search Value (6, 9, 13): \(5.469763045809\)
▸ Incident Central Lines22 lines

{3, 1796}, {9, 51}, {10, 3136}, {25, 220}, {31, 2273}, {37, 209}, {42, 213}, {55, 584}, {63, 295}, {71, 228}, {72, 306}, {101, 199}, {181, 756}, {184, 219}, {200, 1018}, {201, 1425}, {210, 430}, {212, 3270}, {373, 3305}, {511, 3219}, {612, 2295}, {1011, 3190}

▸ Functional Relations2 relations