Trigonometry! #91

Geometry Level 3

If in a \(\Delta ABC\), \[\cos A \cos B + \sin A \sin B \sin C = 1\] then express the ratio \(a:b:c\) in its most simplest form, \(x:y:z\) and enter the value of \(x^{2}+y^{2}+z^{2}\).

This problem is part of the set Trigonometry.

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