X3112

TgX(31)

X3112 = cevapoint of X1 and X75
< 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) { 31, 75 }: Central Line L(31, 75) { 83, 213 }: Central Line L(83, 213) { 42, 308 }: Central Line L(42, 308) { 1, 561 }: Central Line L(1, 561) { 38, 799 }: Central Line L(38, 799) { 689, 741 }: Central Line L(689, 741) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1964 = BICENTRIC SUM OF PU(36) (0.6058, 0.2641) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_75 = ISOTOMIC CONJUGATE OF INCENTER (0.4988, 0.1682) X_83 = CEVAPOINT OF CENTROID AND SYMMEDIAN POINT (0.5651, 0.2360) X_213 = -CEVA CONJUGATE OF X(42) (0.6135, 0.2833) X_42 = CROSSPOINT OF INCENTER AND SYMMEDIAN POINT (0.5880, 0.2495) X_308 = ISOTOMIC CONJUGATE OF X(39) (0.4915, 0.1700) X_1 = INCENTER (0.5714, 0.2333) X_561 = ISOGONAL CONJUGATE OF 4th POWER POINT (0.4126, 0.1125) X_38 = CROSSPOINT OF X(1) AND X(75) (0.5443, 0.1976) X_799 = ISOGONAL CONJUGATE OF X(798) (0.0470, 0.3636) X_689 = TRILINEAR POLE OF LINE X(6)X(76) (0.0585, 0.3579) X_741 = EVEN (- 1, 1) CIRCUMCIRCLE POINT (1.0071, 0.0451) X_3112 = TgX(31) (0.5306, 0.2022) A B C X1964 X31 X75 X83 X213 X42 X308 X1 X561 X38 X799 X689 X741 X3112 (a, b, c) = (5, 6, 7) | AB = 1

X3112 (TgX(31)) 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 \(f(a,b,c) = 1/(a^{2}(b^{2} + c^{2}))\)
Search Value (6, 9, 13): \(2.817984554426\)
▸ Incident Central Lines8 lines

{1, 561}, {31, 75}, {38, 799}, {42, 308}, {83, 213}, {92, 1973}, {689, 741}, {1402, 1441}

▸ Functional Relations8 relations