X1644

TRIPOLAR CENTROID OF X190

X1644 is the tripolar centroid of X190.
< 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) { 1647, 2 }: Nagel Line { 1, 2 }: Nagel Line { 900, 1635 }: Central Line L(900, 1635) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1647 = TRIPOLAR CENTROID OF X(514) (0.9566, 0.6107) X_2 = CENTROID (0.5374, 0.2000) X_1 = INCENTER (0.5714, 0.2333) X_900 = CROSSDIFFERENCE OF X(6) AND X(101) (0.9566, 0.6107) X_1635 = TRIPOLAR CENTROID OF X(1) (2.1429, 2.0996) X_1644 = TRIPOLAR CENTROID OF X(190) (0.1182, -0.2108) A B C X1647 X2 X1 X900 X1635 X1644 (a, b, c) = (5, 6, 7) | AB = 1

X1644 (TRIPOLAR CENTROID OF X190) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\) (see note above X1635)
Search Value (6, 9, 13): \(-6.214871691337\)
▸ Incident Central Lines2 lines

{1, 2}, {900, 1635}

▸ Functional Relations2 relations

  • X1644 = reflection of X1647 in X2

  • X1644 = centroid of Nagel line intercepts with sidelines of ABC