# 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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