Consider the points $O\left(0,0\right),A\left(0,1\right)$ , and $B\left(1,1\right)$ in the $x,y$ plane. Suppose that points $C\left(x,1\right)$ and $D\left(1,y\right)$ are chosen such that $0<x<1$ and such that $O,C$ and $D$ are collinear. Let the sum of the area of triangles $OAC$ and BCD be denoted by $S$ . Then which of the following is/are correct? Minimum value of $S$ is irrational lying in $\left(\frac{1}{3},\frac{1}{2}\right)\dot{}$ Minimum value of $S$ is irrational in $\left(\frac{2}{3},1\right)$ The value of $x$ for the minimum value of $S$ lies in $\left(\frac{2}{3},1\right)\dot{}$ The value of $x$ for the minimum value of $S$ lies in $\left(\frac{1}{3},\frac{1}{2}\right)\dot{}$

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