You can guess but can you prove it?

Geometry Level 2

Identical circles, \(1,2,3\), tangent to each other, are tangent to inner circle \(4\).

Circle \(5\) is tangent to circles \(3,4\) inside it. Line \(A\) passes through the centers of circles \(3, 4, 5\). Line \(B\), perpendicular to Line \(A\), passes through the center of circle \(4\), and intersects circle \(5\) at point \(P\). Line \(C\) passes through point \(P\) and the center of circle \(5\).

Find the small angle between lines \(A\) and \(C\) in degrees.

Note: Line \(C\) does not pass through the centers of circles \(2\) and \(3\)!


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