Consider two points on a Cartesian coordinate system, \(\,\text{A}(-2,1)\) and \(\,\text{B}(0,-3)\). Point \(\,\text{C}\) is then drawn such that \(\overrightarrow{AC}\perp \overrightarrow{BC}\). The expected area of \(\Delta\text{ABC}\) can be expressed as \(\;\frac{a}{b\pi}\), where \(\,a\) and \(\,b\) are positive integers. Calculate \(\,a+b\).

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