X₃₄₈₆

INTERSECTION OF LINES X₁X_4 AND X₈X_21

X₃₄₈₆ = extangents-to-intangents similarity image of X₈

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

X₃₄₈₆ (INTERSECTION OF LINES X₁X_4 AND X₈X_21) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {1, 4}, {8, 21}

• Related Centers: X₁ (INCENTER), X₄ (ORTHOCENTER), X₈ (NAGEL POINT), X₂₁ (SCHIFFLER POINT)

Trilinears: \(f(A,B,C) : f(B,C,A) : f(C,A,B)\), where \(f(A,B,C) = \cos A + \cos B + \cos C - \cos B \cos C\)

Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)

Search Value (6, 9, 13): \(2.443958424586\)

▸ Incident Central Lines21 lines

{1, 4}, {2, 1837}, {3, 1788}, {8, 21}, {11, 2476}, {20, 65}, {25, 1610}, {29, 1857}, {46, 376}, {78, 2551}, {80, 498}, {90, 1000}, {144, 145}, {281, 284}, {452, 960}, {519, 1697}, {529, 2098}, {1159, 1657}, {1468, 1936}, {1503, 1854}, {2268, 2345}

▸ Functional Relations2 relations

• X₃₄₈₆ = reflection of X_i in X_j for these (i,j): (8, 958), (388, 1)

• X₃₄₈₆ = extangents-to-intangents similarity image of X₈