Area Of A Sickle

Geometry Level 4

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 \(DB\), \(BJ\), \(JK\), and \(KD\) can be represented as \[\dfrac{a \pi + b}{c},\] where \(a,b,c\) are integers with \(c\) positive, find the maximum value of \(a+b+c\).

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