X365

SQUARE ROOT POINT

For a construction of X365, see the note at X2, which provides for a construction barycentric square roots which one can easily extend to a construction for trilinear square roots.
< 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, 364 }: Central Line L(1, 364) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_366 = ISOGONAL CONJUGATE OF X(365) (0.5551, 0.2165) X_1 = INCENTER (0.5714, 0.2333) X_364 = WABASH CENTER (EQUAL AREAS ISOSCELIZER POINT) (0.5406, 0.1984) X_365 = SQUARE ROOT POINT (0.5864, 0.2502) A B C X366 X1 X364 X365 (a, b, c) = (5, 6, 7) | AB = 1

X365 (SQUARE ROOT POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(a^{1/2} : b^{1/2} : c^{1/2}\)
Barycentrics: \(a^{3/2} : b^{3/2} : c^{3/2}\)
Search Value (6, 9, 13): \(1.308932882636\)
▸ Incident Central Lines6 lines

{1, 364}, {6, 2118}, {43, 2068}, {292, 2146}, {2110, 2119}, {2144, 2147}

▸ Functional Relations5 relations