X3691

X3294com(EXTOUCH TRIANGLE)

X3691 = excentral-to-ABC barycentric image of X3294
< 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) { 8, 9 }: Central Line L(8, 9) { 10, 672 }: Central Line L(10, 672) { 39, 899 }: Central Line L(39, 899) { 41, 958 }: Central Line L(41, 958) { 388, 966 }: Central Line L(388, 966) { 210, 1212 }: Central Line L(210, 1212) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_8 = NAGEL POINT (0.4694, 0.1333) X_9 = MITTENPUNKT (0.5110, 0.1615) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_672 = CROSSDIFFERENCE OF X(1) AND X(514) (1.9245, 2.2184) X_39 = BROCARD MIDPOINT (0.5778, 0.2305) X_899 = INTERSECTION OF LINES X(1)X(2) AND X(6)X(750) (2.3571, 1.9829) X_41 = -CEVA CONJUGATE OF X(31) (0.5823, 0.2244) X_958 = INTERSECTION OF LINES X(1)X(6) AND X(2)X(12) (0.5166, 0.1682) X_388 = ∩X(7)X(8) (0.5790, 0.2635) X_966 = INTERSECTION OF LINES X(2)X(6) AND X(4)X(9) (0.5191, 0.1803) X_210 = -CEVA CONJUGATE OF X(37) (0.4925, 0.1466) X_1212 = ISOGONAL CONJUGATE OF X(1170) (0.5256, 0.1789) X_3691 = com(EXTOUCH TRIANGLE) (0.5004, 0.1544) A B C X8 X9 X10 X672 X39 X899 X41 X958 X388 X966 X210 X1212 X3691 (a, b, c) = (5, 6, 7) | AB = 1

X3691 (X3294com(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 \(f(a,b,c) = a(b + c - a)(ab + ac + 2bc)\)
Search Value (6, 9, 13): \(3.825803457549\)
▸ Incident Central Lines22 lines

{2, 1475}, {8, 9}, {10, 672}, {39, 899}, {41, 958}, {44, 2295}, {210, 1212}, {213, 1573}, {220, 2654}, {239, 1655}, {388, 966}, {405, 2280}, {519, 3294}, {604, 965}, {960, 2170}, {1018, 3626}, {1055, 2975}, {1107, 1193}, {1213, 2260}, {2276, 3214}, {3219, 3496}, {3501, 3617}

▸ Functional Relations1 relation

  • X3691 = excentral-to-ABC barycentric image of X3294