Trigonometry! #70

Geometry Level 4

If in a \(\Delta ABC\), \[\frac {b+c}{11} = \frac {c+a}{12} = \frac {a+b}{13}\] then \[\frac {\cos A}{x} = \frac {\cos B}{y} = \frac {\cos C}{z}\] where \(x\), \(y\) and \(z\) are coprime positive integers. Enter the value of \(x+y+z\).

This problem is part of the set Trigonometry.

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