X902

CROSSPOINT OF X6 AND X106

X902 is the crosspoint of X6 and X106.
< 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) { 6, 31 }: Central Line L(6, 31) { 1, 89 }: Central Line L(1, 89) { 36, 106 }: Central Line L(36, 106) { 100, 238 }: Central Line L(100, 238) { 187, 237 }: Central Line L(187, 237) { 35, 595 }: Central Line L(35, 595) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_106 = Λ(INCENTER, CENTROID) (1.0000, 0.0000) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_1 = INCENTER (0.5714, 0.2333) X_89 = ISOGONAL CONJUGATE OF X(45) (0.5963, 0.2697) X_36 = INVERSE-IN-CIRCUMCIRCLE OF INCENTER (1.3333, 1.6330) X_100 = ANTICOMPLEMENT OF FEUERBACH POINT (0.1429, 0.4666) X_238 = -LINE CONJUGATE OF X(37) (1.6190, 1.4775) X_187 = INVERSE-IN-CIRCUMCIRCLE OF X(6) (SCHOUTE CENTER) (1.1986, 1.2559) X_237 = -LINE CONJUGATE OF X(2) (0.9894, 1.3825) X_35 = {X(1),X(3)}-HARMONIC CONJUGATE OF X(36) (0.5373, 0.1706) X_595 = 2nd HATZIPOLAKIS-YIU POINT (0.6456, 0.3307) X_902 = CROSSPOINT OF X(6) AND X(106) (1.2500, 1.2247) A B C X6 X106 X31 X1 X89 X36 X100 X238 X187 X237 X35 X595 X902 (a, b, c) = (5, 6, 7) | AB = 1

X902 (CROSSPOINT OF X6 AND X106) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(a(b + c - 2a) : b(c + a - 2b) : c(a + b - 2c) : :\)
Barycentrics: \(a^{2}(b + c - 2a) : b^{2}(c + a - 2b) : c^{2}(a + b - 2c)\)
Search Value (6, 9, 13): \(-2.002622211486\)
▸ Alternate Coordinates1 form

  • Trilinears: \(1 - \cos 2A - (1 + \cos A)(\cos B + \cos C) : :\)

▸ Incident Central Lines12 lines

{1, 89}, {6, 31}, {35, 595}, {36, 106}, {44, 678}, {100, 238}, {109, 840}, {165, 614}, {187, 237}, {518, 896}, {739, 813}, {750, 1001}

▸ Functional Relations13 relations