X₃₂₉₅

INTERSECTION OF LINES X₁X_3 AND X₄X_390

X₃₂₉₅ = midpoint of X₁ and X₁₆₉₇

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

X₃₂₉₅ (INTERSECTION OF LINES X₁X_3 AND X₄X_390) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {1, 1697}

• Related Centers: X₁ (INCENTER), X₁₆₉₇ (INSIMILICENTER)

Trilinears: \(2 + \cos A : 2 + \cos B : 2 + \cos C\)

Barycentrics: \((2 + \cos A)(\sin A) : (2 + \cos B)(\sin B) : (2 + \cos C)(\sin C)\)

Search Value (6, 9, 13): \(2.211234789226\)

▸ Incident Central Lines30 lines

{1, 3}, {4, 390}, {5, 497}, {11, 498}, {12, 381}, {20, 1056}, {21, 145}, {30, 388}, {33, 1598}, {34, 1597}, {73, 1480}, {77, 1059}, {149, 2476}, {172, 1384}, {212, 1497}, {221, 500}, {284, 2256}, {355, 950}, {378, 1398}, {382, 1478}, {474, 1387}, {496, 1058}, {595, 1126}, {601, 1496}, {602, 1263}, {902, 1468}, {916, 2293}, {943, 1260}, {944, 1012}, {1036, 1807}

▸ Functional Relations12 relations

• X₃₂₉₅ = midpoint of X₁ and X₁₆₉₇

• X₃₂₉₅ = isogonal conjugate of X₃₂₉₆

• X₃₂₉₅ = crosssum of X₁ and X₃₃₃₈

• X₃₂₉₅ = crossdifference of every pair of points of the line X₆₅₀X₂₄₂₃

• X₃₂₉₅ = extangents-to-intangents similarity image of X₃

• X₃₂₉₅ = center of circle that is locus of crosssums of incircle antipodes

• X₃₂₉₅ = X₁₅₉₅-of-excentral-triangle

• X₃₂₉₅ = X₁₅₉₃-of-2nd-circumperp-triangle

• X₃₂₉₅ = X₁₁₄₁₄-of-1st-circumperp-triangle

• X₃₂₉₅ = excentral-to-2nd-circumperp similarity image of X₁₆₉₇

• X₃₂₉₅ = homothetic center of inner Yff triangle and cross-triangle of ABC and 2nd Johnson-Yff triangle

• X₃₂₉₅ = {X_i,X_j}-harmonic conjugate of X_k for thewe (i,j,k): (1,3,999), (1,40,942), (55,56,35)