X₃₀₄₈

INTERSECTION X₁₁₀X_126∩X₁₁₁X_184

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

X₃₀₄₈ (INTERSECTION X₁₁₀X_126∩X₁₁₁X_184) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {110, 126}, {111, 184}

• Related Centers: X₁₁₀ (FOCUS OF KIEPERT PARABOLA), X₁₂₆ (-OF-MEDIAL-TRIANGLE), X₁₁₁ (PARRY POINT), X₁₈₄ (INVERSE OF X)

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = a^{3}(a^{4} + b^{4} - c^{4} - 4a^{2}b^{2} + 3b^{2}c^{2})(a^{4} - b^{4} + c^{4} - 4a^{2}c^{2} + 3b^{2}c^{2})\)

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

Search Value (6, 9, 13): \(-1.795450617747\)

X₃₀₄₈ lies on the sine-triple-angle circle.

▸ Incident Central Lines7 lines

{110, 126}, {111, 184}, {1147, 1296}, {2780, 3043}, {2805, 3045}, {2813, 3046}, {2854, 3047}