X209

X4-CEVA CONJUGATE OF X37

X209 = X4-Ceva conjugate of X37
< 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) { 10, 12 }: Central Line L(10, 12) { 6, 31 }: Central Line L(6, 31) { 44, 51 }: Central Line L(44, 51) { 306, 518 }: Central Line L(306, 518) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_4 = ORTHOCENTER (0.6122, 0.3958) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_12 = {X(1),X(5)}-HARMONIC CONJUGATE OF X(11) (0.5641, 0.2407) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_44 = -LINE CONJUGATE OF X(1) (2.1429, 2.0996) X_51 = CENTROID OF ORTHIC TRIANGLE (0.6093, 0.3186) X_306 = ISOTOMIC CONJUGATE OF X(27) (0.3924, 0.0579) X_518 = ISOGONAL CONJUGATE OF X(105) (0.9154, 0.6489) X_209 = -CEVA CONJUGATE OF X(37) (0.7303, 0.4592) A B C X4 X37 X10 X12 X6 X31 X44 X51 X306 X518 X209 (a, b, c) = (5, 6, 7) | AB = 1

X209 (X4-CEVA CONJUGATE OF X37) 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 \(f(A,B,C) = (\sin B + \sin C)[\sin A + \sin(A - B) + \sin(A - C)]\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(-2.027998688698\)
▸ Incident Central Lines4 lines

{6, 31}, {10, 12}, {44, 51}, {306, 518}

▸ Functional Relations2 relations