X₈₄₈

YIU ANGLE POINT

angle BXC : angle CXA : angle AXB =\(a : b : c\).

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

X₈₄₈ (YIU ANGLE POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Trilinears: \((\csc A)/(\cot A - \cot A') : :\), where \(A' = 2\pi a/(a + b + c)\)

Barycentrics: \(g(A,B,C) : g(B,C,A) : g(C,A,B)\), where \(g(A,B,C) = 1/(\cot A - \cot A')\), \(A' = 2\pi a/(a + b + c)\)

Search Value (6, 9, 13): \(2.959966790242\)

Notes

X₈₄₈ point is introduced by Paul Yiu in Hyacinthos #2704, April 7, 2001 (see also #2708, April 10, 2001) as the solution X of the equation