Larry The Lamb

Geometry Level 2

A square field \(ABCD\) has center \(O\) and side length \(2l\). A rope of length \(l\) connects Larry the lamb at one end to \(O\) at the other end.

The perpendicular from \(O\) to side \(AD\) forms a wall that Larry cannot pass through. The point \(P\) that is the midpoint of the perpendicular from \(O\) to \(DC\) forms a peg that will catch on the rope.

What percentage of the field can Larry walk on, to the nearest percent?

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