X₃₂₇₈

PERSPECTOR OF TRIANGLES M1M2M3 AND T1T2T3

X₃₂₇₈ is the perspector of triangles m1m2m3 and t1t2t3.

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

X₃₂₇₈ (PERSPECTOR OF TRIANGLES M1M2M3 AND T1T2T3) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {3, 356}, {16, 358}

• Related Centers: X₃ (CIRCUMCENTER), X₃₅₆ (MORLEY CENTER), X₁₆ (2nd ISODYNAMIC POINT), X₃₅₈ (2nd MORLEY-TAYLOR-MARR CENTER)

Trilinears: \(f(A,B,C) : f(B,C,A) : f(C,A,B)\), where \(f(A,B,C) = \cos(A/3) \cos(2A/3) + \cos(B/3) \cos(C/3)\)

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

Search Value (6, 9, 13): \(2.041763577641\)

▸ Incident Central Lines2 lines

{3, 356}, {16, 358}