# 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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