X3772

X1707com[T(a², a² - c²)]

X3772 = complement of X345
< A B C >: Reference Triangle △ABC < M_a M_b M_c >: Medial Triangle △M_a M_b M_c [ A B ]: Sideline AB (Base c = 1) [ B C ]: Sideline BC (Side a) [ C A ]: Sideline CA (Side b) { 2, 345 }: Central Line L(2, 345) { 2, 37 }: Central Line L(2, 37) { 11, 33 }: Central Line L(11, 33) { 6, 226 }: Central Line L(6, 226) { 56, 225 }: Central Line L(56, 225) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) M_a = Midpoint M_a of BC (0.8061, 0.2999) M_b = Midpoint M_b of CA (0.3061, 0.2999) M_c = Midpoint M_c of AB (0.5000, 0.0000) X_2 = CENTROID (0.5374, 0.2000) X_345 = ISOTOMIC CONJUGATE OF X(278) (0.3405, 0.0381) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_11 = FEUERBACH POINT (0.7347, 0.0667) X_33 = PERSPECTOR OF THE ORTHIC AND INTANGENTS TRIANGLES (0.6019, 0.3546) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_226 = -CEVA CONJUGATE OF X(65) (0.5778, 0.2588) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_225 = -CEVA CONJUGATE OF X(65) (0.6246, 0.4451) X_3772 = com[T(a2, a2 - c2)] (0.6359, 0.2809) A B C Ma Mb Mc X2 X345 X37 X11 X33 X6 X226 X56 X225 X3772 (a, b, c) = (5, 6, 7) | AB = 1

X3772 (X1707com[T(a², a² - c²)]) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Barycentrics: \(a^{3} + b^{3} + c^{3} - b^{2}c - c^{2}b : :\)
Search Value (6, 9, 13): \(0.982553601404\)
▸ Incident Central Lines37 lines

{1, 442}, {2, 37}, {4, 1104}, {6, 226}, {11, 33}, {27, 1333}, {31, 1836}, {44, 329}, {55, 3011}, {56, 225}, {57, 1020}, {72, 1714}, {172, 379}, {220, 3008}, {223, 3554}, {278, 393}, {387, 3487}, {475, 3086}, {497, 1279}, {516, 3052}, {528, 3749}, {851, 2352}, {899, 2318}, {908, 2911}, {946, 1191}, {1072, 3428}, {1125, 2049}, {1201, 2654}, {1284, 3185}, {1329, 1722}, {1376, 1738}, {1612, 3651}, {2218, 3145}, {2887, 3416}, {2999, 3553}, {3191, 3216}, {3434, 3744}

▸ Functional Relations4 relations

  • X3772 = complement of X345

  • X3772 = barycentric product X1*X17861

  • X3772 = polar conjugate of X34406

  • X3772 = trilinear pole of the polar, wrt the Fuhrmann circle, of the perspector of the Fuhrmann circle

Notes

X3772 is the center of the inconic that is the polar conjugate of the isotomic conjugate of the incircle. (Randy Hutson, October 15, 2018)