X1250

ISOGONAL CONJUGATE OF X1081

X1250 is the isogonal conjugate of X1081.
< 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) { 1, 16 }: Central Line L(1, 16) { 6, 31 }: Central Line L(6, 31) { 15, 35 }: Central Line L(15, 35) { 37, 1251 }: Central Line L(37, 1251) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1081 = POINT ALPHECCA (0.6056, 0.3226) X_1 = INCENTER (0.5714, 0.2333) X_16 = 2nd ISODYNAMIC POINT (1.8453, 2.3239) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_15 = 1st ISODYNAMIC POINT (0.5519, 0.1878) X_35 = {X(1),X(3)}-HARMONIC CONJUGATE OF X(36) (0.5373, 0.1706) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_1251 = ISOGONAL CONJUGATE OF X(1082) (0.5908, 0.2784) X_1250 = ISOGONAL CONJUGATE OF X(1081) (0.5229, 0.1536) A B C X1081 X1 X16 X6 X31 X15 X35 X37 X1251 X1250 (a, b, c) = (5, 6, 7) | AB = 1

X1250 (ISOGONAL CONJUGATE OF X1081) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(1/f(a,b,c) : 1/f(b,c,a) : 1/f(c,a,b)\), where f(a,b,c) is as in X1081
Search Value (6, 9, 13): \(3.421979587480\)
▸ Alternate Coordinates1 form

  • Trilinears: \(g(A,B,C) : g(B,C,A) : g(C,A,B)\), where \(g(A, B, C) = \cos(A/2) \cos(A/2 + \pi /6)\)

▸ Incident Central Lines4 lines

{1, 16}, {6, 31}, {15, 35}, {37, 1251}

▸ Functional Relations3 relations