Comprehension A circle \( C \) whose radius is 1 unit, touches the \( x \)-axis at point \( A \)...

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Comprehension
A circle \( C \) whose radius is 1 unit, touches the \( x \)-axis at point \( A \). The centre \( Q \) of \( C \) lies in first quadrant. The tangent from origin \( O \) to the circle touches it at \( T \) and a point \( P \) lies on it such that \( \triangle O A P \) is a right angled triangle at \( A \) and its perimeter is 8 units.
Equation of circle \( C \) is
(a) \( \{x-(2+\sqrt{3})\}^{2}+(y-1)^{2}=1 \)
(b) \( \{x-(\sqrt{3}+\sqrt{2})\}^{2}+(y-1)^{2}=1 \)
(c) \( (x-2)^{2}+(y-1)^{2}=1 \)
(d) \( (x-\sqrt{3})^{2}+(y+2)^{2}=1 \)
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