How much does it occupy?

Geometry Level 4

Let, \(d(P,AB)\) denote the distance perpendicular between the point \(P\) and the line \(AB\).

Let \(OABC\) be a rectangle with \(O\) as the origin and \(A \equiv (3,0)\), \(B \equiv (3,2)\), \(C \equiv (0,2)\). And let \(P\) be point in the rectangle that is subjected to

\[d(P,OA) < \text{min} \left[d(P,AB),d(P,BC),d(P,OC)\right]\]

Find the area of the region of points satisfying the point \(P\).


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