X₁₁₆₀

CIRCUMCENTER OF OUTER GREBE TRIANGLE

X₁₁₆₀ is the circumcenter of outer grebe triangle.

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

X₁₁₆₀ (CIRCUMCENTER OF OUTER GREBE TRIANGLE) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {1161, 3}

• Related Centers: X₁₁₆₁ (CIRCUMCENTER OF INNER GREBE TRIANGLE), X₃ (CIRCUMCENTER)

Trilinears: \((1 + 2 \cot A + 2 \cot B + 2 \cot C) \cos A - 2 \sin A : :\)

Search Value (6, 9, 13): \(41.767184322768\)

▸ Alternate Coordinates1 form

• Trilinears: \(s (1 + 2 \cot \omega ) \cos A - 2 \sin A : :\)

▸ Incident Central Lines2 lines

{3, 6}, {4, 1162}

▸ Functional Relations1 relation

• X₁₁₆₀ = reflection of X₁₁₆₁ in X₃

Notes

See Hyacinthos #6537.

Let O_A be the circle centered at the A-vertex of the anti-inner-Grebe triangle and passing through A; define O_B and O_C cyclically. X₁₁₆₀ is the radical center of O_A, O_B, O_C. (Randy Hutson, August 28, 2020)