X2982

DC(X21)

X2982 = crosssum of X1 and X2954
< 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) { 28, 65 }: Central Line L(28, 65) { 48, 57 }: Central Line L(48, 57) { 1, 201 }: Central Line L(1, 201) { 2, 219 }: Central Line L(2, 219) { 6, 278 }: Central Line L(6, 278) { 222, 279 }: Central Line L(222, 279) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_28 = CEVAPOINT OF X(19) AND X(25) (0.6285, 0.4382) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_48 = CROSSPOINT OF X(1) AND X(63) (0.5412, 0.1246) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_1 = INCENTER (0.5714, 0.2333) X_201 = -CEVA CONJUGATE OF X(12) (0.4897, 0.1062) X_2 = CENTROID (0.5374, 0.2000) X_219 = -CEVA CONJUGATE OF X(55) (0.4277, 0.0625) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_278 = ISOGONAL CONJUGATE OF X(219) (0.6278, 0.4577) X_222 = -CEVA CONJUGATE OF X(56) (0.5653, 0.1568) X_279 = ISOGONAL CONJUGATE OF X(220) (0.6236, 0.3540) X_2982 = DC(X(21)) (0.6020, 0.2808) A B C X28 X65 X48 X57 X1 X201 X2 X219 X6 X278 X222 X279 X2982 (a, b, c) = (5, 6, 7) | AB = 1

X2982 (DC(X21)) 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) is as given just before X2979, using U = X21
Search Value (6, 9, 13): \(0.679892777417\)
▸ Alternate Coordinates1 form

  • Trilinears: \(1/((b + c) \cos A + b \cos B + c \cos C) : :\)

▸ Incident Central Lines12 lines

{1, 201}, {2, 219}, {6, 278}, {28, 65}, {48, 57}, {55, 955}, {81, 1214}, {222, 279}, {274, 1231}, {1002, 1617}, {1396, 1409}, {1630, 1730}

▸ Functional Relations3 relations