X₂₅₆₄

INSIMILICENTER(INCIRCLE, 2nd BROCARD CIRCLE)

X₂₅₆₄ is the insimilicenter(incircle, 2nd Brocard circle).

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

X₂₅₆₄ (INSIMILICENTER(INCIRCLE, 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}, {1342, 1675}

• Related Centers: X₁ (INCENTER), X₃ (CIRCUMCENTER), X₁₃₄₂ (INSIMILICENTER), X₁₆₇₅ (EXSIMILICENTER)

Trilinears: \(f(A,B,C) : f(B,C,A) : f(C,A,B)\), where \(f(A,B,C) = e + \cos A\), where \(e = (1 - 4 \sin^{2}\omega )^{1/2}\)

Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)

Search Value (6, 9, 13): \(2.844199590750\)

▸ Incident Central Lines13 lines

{1, 3}, {2, 2569}, {8, 2568}, {11, 2566}, {12, 2567}, {1124, 2561}, {1335, 2560}, {1342, 1675}, {1343, 1674}, {1672, 2559}, {1673, 2558}, {2007, 2563}, {2008, 2562}