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Let \( O(0,0), A(2,0) \) and \( B\left(1, \frac{1}{\sqrt{3}}\right) \) be the vertices of a triangle.
\( \mathrm{P} \)
Let \( R \) be the region consisting of all those points \( P \) inside \( \triangle O A B \)
W. satisfying.
\( d(P, O A) \leq \min \{d(P, O B), d(P, A B)\} \), where, \( d \) denotes the
distance from the point \( P \) to the corresponding line. Let \( M \) be the peak of region \( R \).
The area of region \( R \) is equal to
(a) \( 2-\sqrt{3} \)
(b) \( 2+\sqrt{3} \)
(c) \( 2 \sqrt{3} \)
(d) \( 4+\sqrt{3} \)
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