X₁₅₁₅

ORTHOJOIN OF X₄

X₁₅₁₅ = intersection of Simson line of X₁₀₇ (line X₁₃₃X₁₅₁₅) and trilinear polar of X₁₀₇ (line X₄X₆)

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

X₁₅₁₅ (ORTHOJOIN OF X₄) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {4, 6}, {30, 1294}

• Related Centers: X₄ (ORTHOCENTER), X₆ (SYMMEDIAN POINT), X₃₀ (EULER INFINITY POINT), X₁₂₉₄ (COLLINGS TRANSFORM OF X₁₂₂)

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\) (see note above X₁₅₁₂)

Search Value (6, 9, 13): \(-7.150597995560\)

X₁₅₁₅ lies on the Simson quartic (Q101).

▸ Incident Central Lines4 lines

{4, 6}, {30, 1294}, {133, 1559}, {297, 1533}

▸ Functional Relations1 relation

• X₁₅₁₅ = intersection of Simson line of X₁₀₇ (line X₁₃₃X₁₅₁₅) and trilinear polar of X₁₀₇ (line X₄X₆)