# Circle on a Strip

Calculus Level 3

I have a infinitely long strip of paper that is one unit wide. On the paper is a point $$P$$ that is $$\dfrac{1}{4}$$ units away from one of the edges of the strip.

Let $$L$$ be the locus of all points $$O$$ such that if I draw the circle with center $$O$$ passing through $$P$$, the entire circle can be drawn on the strip of paper. If the area of $$L$$ can be expressed by $$\dfrac{a\sqrt{b}}{c}$$ for relatively prime $$a,c$$ and square-free $$b$$, then find $$a+b+c$$.

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