X3634

H⁻¹(X10; M, 2)

X3634 = centroid of ABCX10
< 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, 2 }: Nagel Line { 5, 516 }: Central Line L(5, 516) { 140, 515 }: Central Line L(140, 515) { 44, 1213 }: Central Line L(44, 1213) { 88, 1224 }: Central Line L(88, 1224) { 474, 993 }: Central Line L(474, 993) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1 = INCENTER (0.5714, 0.2333) X_2 = CENTROID (0.5374, 0.2000) X_5 = NINE-POINT CENTER (0.5561, 0.2489) X_516 = ISOGONAL CONJUGATE OF X(103) (0.7703, 0.7386) X_140 = MIDPOINT OF X(3) AND X(5) (0.5281, 0.1755) X_515 = ISOGONAL CONJUGATE OF X(102) (0.6804, 0.7691) X_44 = -LINE CONJUGATE OF X(1) (2.1429, 2.0996) X_1213 = ISOGONAL CONJUGATE OF X(1171) (0.5294, 0.1914) X_88 = ISOGONAL CONJUGATE OF X(44) (1.0000, 0.0000) X_1224 = ISOGONAL CONJUGATE OF X(1203) (0.5326, 0.1960) X_474 = EULER LINE INTERCEPT OF LINE X(10)X(56) (0.5441, 0.2176) X_993 = MIDPOINT OF X(1) AND X(63) (0.5140, 0.1578) X_3634 = H-1(X(10); M, 2) (0.5332, 0.1958) A B C X1 X2 X5 X516 X140 X515 X44 X1213 X88 X1224 X474 X993 X3634 (a, b, c) = (5, 6, 7) | AB = 1

X3634 (H⁻¹(X10; M, 2)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(bc(2a + 3b + 3c) : :\)
Barycentrics: \(2a + 3b + 3c : 2b + 3c + 3a : 2c + 3a + 3b\)
Search Value (6, 9, 13): \(2.746751327868\)
▸ Alternate Coordinates1 form

  • Trilinears: \(r - 6 R \sin B \sin C : :\)

▸ Linear Combinations1 combination
▸ Incident Central Lines21 lines

{1, 2}, {5, 516}, {37, 1574}, {40, 3090}, {44, 1213}, {46, 3305}, {88, 1224}, {140, 515}, {165, 3091}, {355, 3526}, {442, 1155}, {451, 1861}, {474, 993}, {632, 1385}, {750, 1724}, {944, 3533}, {946, 1656}, {1739, 2292}, {3039, 3161}, {3219, 3336}, {3525, 3576}

▸ Functional Relations10 relations