A) \[\sqrt{5}\]
B) \[1\]
C) \[\sqrt{2}\]
D) \[2\]
Correct Answer: D
Solution :
Equation of the line through the given points is \[y-3=x-2\Rightarrow x-y+1=0\] Equation of the perpendicular line through the midpoint \[(3,4)\] is\[x+y-7=0\]. This intersects the given line at the center of the circle. So, the center of the circle is found to be \[(2,5)\]. Clearly, the radius is then \[\sqrt{{{({{x}_{2}}-{{x}_{1}})}^{2}}+{{({{y}_{2}}-{{y}_{1}})}^{2}}}=\sqrt{{{(2-2)}^{2}}+{{(3-5)}^{2}}}=2\]units . So the answer is option D.
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