X₄₈₇

ANTICOMPLEMENT OF X₄₈₆

X₄₈₇ is the anticomplement of X₄₈₆.

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

X₄₈₇ (ANTICOMPLEMENT OF X₄₈₆) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {486, 642}

• Related Centers: X₄₈₆ (INNER VECTEN POINT), X₆₄₂ (COMPLEMENT OF X₄₈₆)

Trilinears: \(f(A,B,C) : f(B,C,A) : f(C,A,B)\), where \(f(A,B,C) = (\cos A)(1 - \csc A \sin B \sin C)\)

Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)

Search Value (6, 9, 13): \(4.179064973709\)

▸ Alternate Coordinates1 form

• Barycentrics: \((b^{2} + c^{2} - a^{2})(a^{2} - 2\sigma ) : (c^{2} + a^{2} - b^{2})(b^{2} - 2\sigma ) : (a^{2} + b^{2} - c^{2})(c^{2} - 2\sigma )\) (M. Iliev, 5/13/07)

▸ Incident Central Lines7 lines

{2, 371}, {3, 69}, {4, 489}, {20, 638}, {193, 372}, {376, 490}, {492, 631}

▸ Functional Relations7 relations

• X₄₈₇ = reflection of X₄₈₆ in X₆₄₂

• X₄₈₇ = anticomplement of X₄₈₆

• X₄₈₇ = anticomplementary conjugate of X₆₃₈

• X₄₈₇ = X_i-Ceva conjugate of X_j for these (i,j): (4, 488), (489, 20), (491, 2)

• X₄₈₇ = isogonal conjugate of X₈₉₄₆

• X₄₈₇ = X₂₀-of-inner-Vecten-triangle

• X₄₈₇ = orthologic center of outer Vecten to inner Vecten triangles

Notes

X₄₈₇ is a perspector of triangles associated with squares that circumscribe ABC. (Floor van Lamoen, 4/29/98)

Let O_A be the circle centered at the A-vertex of the inner Vecten triangle and passing through A; define O_B and O_C cyclically. X₄₈₇ is the radical center of O_A, O_B, O_C. (Randy Hutson, August 30, 2020)