X₂₅₇₃

EXSIMILICENTER(BEVAN, 2nd BROCARD CIRCLE)

X₂₅₇₃ is the exsimilicenter(Bevan, 2nd Brocard circle).

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

X₂₅₇₃ (EXSIMILICENTER(BEVAN, 2nd BROCARD CIRCLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {1, 3}, {9, 2568}

• Related Centers: X₁ (INCENTER), X₃ (CIRCUMCENTER), X₉ (MITTENPUNKT), X₂₅₆₈ (INSIMILICENTER)

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = 1 - \cos B - \cos C + (1 - 2/e)\cos A\), 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): \(3.541277838844\)

▸ Incident Central Lines13 lines

{1, 3}, {9, 2568}, {1342, 1704}, {1343, 1705}, {1698, 2566}, {1699, 2567}, {1700, 2558}, {1701, 2559}, {1702, 2560}, {1703, 2561}, {1706, 2569}, {2017, 2562}, {2018, 2563}