Area Of A Sickle

Geometry Level 3

In the above diagram, each of the grid squares is a unit long. Also, all the arcs are quadrants. If the area of the shape enclosed by arcs DBDB, BJBJ, JKJK, and KDKD can be represented as aπ+bc,\dfrac{a \pi + b}{c}, where a,b,ca,b,c are integers with cc positive, find the maximum value of a+b+ca+b+c.

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