Circles

Geometry Level 3

Let there be circles \(\Omega_1\), \(\omega\) and \(\Omega_2\) with centers \(O_1\), \(O_3\) and \(O_2\) respectively such that the lines \(O_1AA'\) and \(O_1BB'\) are tangent to circle \(\omega\) at points \(A\) and \(B\) and also to circle \(\Omega_2\) at \(A'\) and \(B'\). Besides, the lines \(O_2CC'\) and \(O_2DD'\) are also tangent to circle \(\omega\) at points \(C\) and \(D\) and also to circle \(\Omega_1\) at \(C'\) and \(D'\). The points \(A\), \(B\), \(C\) and \(D\) lie on the circle \(\omega\) in that order. Find the value of \(\angle{O_3O_1A}\) \(+\) \(\angle{DO_2O_3}\) \(-\) \(\angle{BO_3C}\).

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