You can guess but can you prove it?

Geometry Level 2

Identical circles, 1,2,31,2,3, tangent to each other, are tangent to inner circle 44.

Circle 55 is tangent to circles 3,43,4 inside it. Line AA passes through the centers of circles 3,4,53, 4, 5. Line BB, perpendicular to Line AA, passes through the center of circle 44, and intersects circle 55 at point PP. Line CC passes through point PP and the center of circle 55.

Find the small angle between lines AA and CC in degrees.

Note: Line CC does not pass through the centers of circles 22 and 33!


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