A) \[10\]
B) \[15\]
C) \[5\]
D) none of these
Correct Answer: A
Solution :
Key Idea: If a point is outside the circle, then the greatest distance is equal to the length of diameter and lowest distance between the circle and a point. Since,\[{{S}_{1}}={{10}^{2}}+{{7}^{2}}-4\times 10-2\times 7-20>0.\] So, \[P\] lies outside the circle. Join \[P\] with the centre \[C\,(2,\,\,1)\] of the given circle. Suppose \[PC\] cuts the circle at \[A\] and\[B\], then \[PB\] is the greatest distance of \[P\] from the circle. Now, \[PC=\sqrt{{{(10-2)}^{2}}+{{(7-1)}^{2}}}=10\] \[BC=\sqrt{4+1+20}=5\] \[PB=PC+CB\] \[=10+5=15\]You need to login to perform this action.
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