X₃₅₁₄

INVERSE-IN-CIRCUMCIRCLE OF X₃₅₁₃

X₃₅₁₄ = circumcircle-inverse of X₃₅₁₃

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

X₃₅₁₄ (INVERSE-IN-CIRCUMCIRCLE OF X₃₅₁₃) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {3513, 3660}

• Related Centers: X₃₅₁₃ (1st DILATION CENTER), X₃₆₆₀ (MIDPOINT OF {X₃₅₁₃, X₃₅₁₄})

Trilinears: \((a - b + c)(a + b - c) - 4r(r^{2} + 4rR)^{1/2} : :\) (Peter Moses, 7/24/08)

Tripolars: \(1/r_{a} : :\), where \(r_{a}\), \(r_{b}\), \(r_{c}\) are the exradii

Search Value (6, 9, 13): \(-1.246261237787\)

▸ Alternate Coordinates2 forms

• Tripolars: \(\tan A' : :\), where J_aJ_bJ_c is the excentral triangle

• Tripolars: \(b + c - a : :\)

▸ Linear Combinations1 combination

• X₃₅₁₄ = \((r + 2R - \sqrt{r^{2} + 4rR})\) X₁ - \(2r\) X₃

▸ Incident Central Lines1 line

{1, 3}

▸ Functional Relations5 relations

• X₃₅₁₄ = reflection of X₃₅₁₃ in X₃₆₆₀

• X₃₅₁₄ = circumcircle-inverse of X₃₅₁₃

• X₃₅₁₄ = incircle-inverse of X₃₅₁₃

• X₃₅₁₄ = one of two harmonic traces of the Soddy circles; the other is X₃₅₁₃

• X₃₅₁₄ = {X_i,X_j}-harmonic conjugate of X₃₅₁₃ for these (i,j): (1, 57), (3, 1617), (36, 2078), (55, 56), (65, 354), (165, 1420)

Notes

Like X₃₅₁₃, the point X₃₅₁₄ is the point of intersection of three similar ellipses, each having two of the points A, B, C as foci. (Contributed by Peter Moses, 7/24/08)