X958

INTERSECTION OF LINES X1X_6 AND X2X_12

X958 = complement of X388
< 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, 388 }: Central Line L(2, 388) { 1, 6 }: Incenter–Symmedian Line { 3, 10 }: Central Line L(3, 10) { 2, 12 }: Central Line L(2, 12) { 8, 21 }: Central Line L(8, 21) 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_388 = ∩X(7)X(8) (0.5790, 0.2635) X_1 = INCENTER (0.5714, 0.2333) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_12 = {X(1),X(5)}-HARMONIC CONJUGATE OF X(11) (0.5641, 0.2407) X_8 = NAGEL POINT (0.4694, 0.1333) X_21 = SCHIFFLER POINT (0.5287, 0.1771) X_958 = INTERSECTION OF LINES X(1)X(6) AND X(2)X(12) (0.5166, 0.1682) A B C Ma Mb Mc X2 X388 X1 X6 X3 X10 X12 X8 X21 X958 (a, b, c) = (5, 6, 7) | AB = 1

X958 (INTERSECTION OF LINES X1X_6 AND X2X_12) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

  • Derived Triangle: Medial Triangle △MaMbMc — vertices Ma, Mb, Mc (Formed by the midpoints of sides BC, CA, AB)

  • Central Lines: {2, 388}

  • Related Centers: X2 (CENTROID), X388 (∩X7X8)

Trilinears: \((b + c - a)(a^{2} + ab + ac + 2bc) : :\)
Barycentrics: \(b + c + a \cos A : :\)
Search Value (6, 9, 13): \(3.475723891569\)
▸ Linear Combinations3 combinations
▸ Incident Central Lines15 lines

{1, 6}, {2, 12}, {3, 10}, {8, 21}, {28, 281}, {36, 474}, {40, 1012}, {48, 965}, {63, 65}, {78, 210}, {104, 631}, {198, 966}, {243, 318}, {452, 497}, {944, 1006}

▸ Functional Relations6 relations