X₁₃₇₁

1st RIGBY POINT

X₁₃₇₁ = {X₁,X₇}-harmonic conjugate of X₁₃₇₂

5, 6, 7 3, 4, 5 Kepler Kimberling

X₁₃₇₁ (1st RIGBY POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {1, 7}

• Related Centers: X₁₃₇₂ (2nd RIGBY POINT), X₁ (INCENTER), X₇ (GERGONNE POINT)

Trilinears: \(1 + 8(\operatorname{area} ABC)/[3a(b + c - a)] : :\)

Search Value (6, 9, 13): \(1.123666538485\)

▸ Linear Combinations1 combination

• X₁₃₇₁ = \(3s\) X₁ + \((2r + 8R)\) X₇

▸ Incident Central Lines1 line

{1, 7}

▸ Functional Relations2 relations

• X₁₃₇₁ = {X₁,X₇}-harmonic conjugate of X₁₃₇₂

• X₁₃₇₁ = {X₁₇₆,X₄₈₂}-harmonic conjugate of X₁

Notes

Adrian Oldknow, “The Euler-Gergonne-Soddy Triangle of a Triangle,” American Mathematical Monthly 103 (1996) 319-329. See page 326.

See also MathWorld, Rigby Points.