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 PP that is 14\dfrac{1}{4} units away from one of the edges of the strip.

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

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