X₁₆₇₈

INSIMILICENTER(BROCARD CIRCLE, SPIEKER CIRCLE)

X₁₆₇₈ is the insimilicenter(Brocard circle, Spieker circle).

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

X₁₆₇₈ (INSIMILICENTER(BROCARD CIRCLE, SPIEKER CIRCLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {10, 182}, {2, 1675}

• Related Centers: X₁₀ (SPIEKER CENTER), X₁₈₂ (MIDPOINT OF BROCARD DIAMETER), X₂ (CENTROID), X₁₆₇₅ (EXSIMILICENTER)

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = bc[e(b + c) + a \cos(A - \omega )]\)

Barycentrics: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where \(g(a,b,c) = e(b + c) + a \cos(A - \omega )\)

Search Value (6, 9, 13): \(3.270549514296\)

▸ Incident Central Lines14 lines

{2, 1675}, {8, 1674}, {9, 1705}, {10, 182}, {958, 1341}, {1329, 1348}, {1340, 1376}, {1377, 1668}, {1378, 1669}, {1573, 2034}, {1574, 2033}, {1704, 1706}, {2011, 2014}, {2012, 2013}