X3728

X192com(INCENTRAL TRIANGLE)

X3728 = anticomplement wrt incentral triangle of X2667
< 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) { 37, 42 }: Central Line L(37, 42) { 38, 75 }: Central Line L(38, 75) { 8, 192 }: Central Line L(8, 192) { 31, 1778 }: Central Line L(31, 1778) { 668, 1221 }: Central Line L(668, 1221) { 9, 2209 }: Central Line L(9, 2209) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_42 = CROSSPOINT OF INCENTER AND SYMMEDIAN POINT (0.5880, 0.2495) X_38 = CROSSPOINT OF X(1) AND X(75) (0.5443, 0.1976) X_75 = ISOTOMIC CONJUGATE OF INCENTER (0.4988, 0.1682) X_8 = NAGEL POINT (0.4694, 0.1333) X_192 = -CEVA CONJUGATE OF X(2) (CONGRUENT PARALLELIANS POINT) (0.6147, 0.2635) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_1778 = MIMOSA TRANSFORM OF X(1171) (0.7708, 0.4831) X_668 = TRILINEAR POLE OF LINE X(2)X(37) (0.0159, 0.3302) X_1221 = ISOGONAL CONJUGATE OF X(1197) (0.5249, 0.1927) X_9 = MITTENPUNKT (0.5110, 0.1615) X_2209 = -ISOCONJUGATE OF X(330) (0.6618, 0.3583) X_3728 = com(INCENTRAL TRIANGLE) (0.5332, 0.1904) A B C X37 X42 X38 X75 X8 X192 X31 X1778 X668 X1221 X9 X2209 X3728 (a, b, c) = (5, 6, 7) | AB = 1

X3728 (X192com(INCENTRAL 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 \(f(a,b,c) = a(b + c)(ab^{2} + ac^{2} + bc^{2} + cb^{2})\)
Search Value (6, 9, 13): \(2.717069996347\)
▸ Linear Combinations1 combination
▸ Incident Central Lines11 lines

{8, 192}, {9, 2209}, {31, 1778}, {37, 42}, {38, 75}, {518, 2650}, {668, 1221}, {1107, 2309}, {1213, 3122}, {1573, 2388}, {2269, 2310}

▸ Functional Relations1 relation

  • X3728 = anticomplement wrt incentral triangle of X2667