X₂₅₆₉

EXSIMILICENTER(SPIEKER CIRCLE, 2nd BROCARD CIRCLE)

X₂₅₆₉ is the exsimilicenter(Spieker circle, 2nd Brocard circle).

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

X₂₅₆₉ (EXSIMILICENTER(SPIEKER CIRCLE, 2nd BROCARD CIRCLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {3, 10}, {2, 2564}

• Related Centers: X₃ (CIRCUMCENTER), X₁₀ (SPIEKER CENTER), X₂ (CENTROID), X₂₅₆₄ (INSIMILICENTER)

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = bc[(b + c)e - a \cos A]\), where \(e = (1 - 4 \sin^{2}\omega )^{1/2}\)

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

Search Value (6, 9, 13): \(2.466640551496\)

▸ Incident Central Lines14 lines

{2, 2564}, {3, 10}, {8, 2565}, {9, 2572}, {1329, 2567}, {1342, 1678}, {1343, 1679}, {1377, 2560}, {1378, 2561}, {1680, 2558}, {1681, 2559}, {1706, 2573}, {2013, 2562}, {2014, 2563}