Consider the points \( O(0,0), A(0,1) \), and \( B(1,1) \) in the \...

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Consider the points \( O(0,0), A(0,1) \), and \( B(1,1) \) in the \( x-y \) plane. Suppose that points \( C(x, 1) \) and \( D(1, y) \) are chosen
\( \mathrm{P} \) such that \( 0x1 \) and such that \( O, C \), and \( D \) are collinear.

W Let the sum of the area of triangles \( O A C \) and \( B C D \) be denoted by \( S \). Then which of the following is/are correct?
(1) Minimum value of \( S \) is irrational lying in \( (1 / 3,1 / 2) \).
(2) Minimum value of \( S \) is irrational in \( (2 / 3,1) \).
(3) The value of \( x \) for the minimum value of \( S \) lies in \( (2 / 3,1) \)
(4) The value of \( x \) for the minimum values of \( S \) lies in \( (1 / 3,1 / 2) \).
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