X3635

H⁻¹(X10; M, -1/2)

Recalling that triangle centers are functions, at (a,b,c) = (6,9,13), the values of X3635 and X15519 are equal.
< 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 { 65, 3892 }: Central Line L(65, 3892) { 72, 3898 }: Central Line L(72, 3898) { 3555, 3962 }: Central Line L(3555, 3962) 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_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_3892 = com[INVERSE(n(3rd EULER TRIANGLE))] (0.5993, 0.2699) X_72 = ISOGONAL CONJUGATE OF X(28) (0.4367, 0.0733) X_3898 = com[INVERSE(n(4th EULER TRIANGLE))] (0.5435, 0.1966) X_3555 = DOSA POINT (0.7061, 0.3933) X_3962 = com(EXTOUCH TRIANGLE) (0.2694, -0.1466) X_3635 = H-1(X(10); M, -1/2) (0.5969, 0.2583) A B C X1 X2 X65 X3892 X72 X3898 X3555 X3962 X3635 (a, b, c) = (5, 6, 7) | AB = 1

X3635 (H⁻¹(X10; M, -1/2)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(bc(6a - b - c) : :\)
Barycentrics: \(6a - b - c : 6b - c - a : 6c - a - b\)
Search Value (6, 9, 13): \(0.986013297183\)
▸ Alternate Coordinates1 form

  • Trilinears: \(7 r - 2 R \sin B \sin C : :\)

▸ Linear Combinations1 combination
▸ Incident Central Lines21 lines

{1, 2}, {6, 4029}, {20, 11224}, {21, 13602}, {37, 4700}, {44, 4982}, {65, 3892}, {72, 3898}, {75, 4909}, {86, 4464}, {149, 5270}, {214, 13996}, {355, 5072}, {392, 4005}, {405, 8162}, {726, 4718}, {2796, 4409}, {2802, 9945}, {3555, 3962}, {3630, 5847}, {4072, 4898}

▸ Functional Relations5 relations