tmua.me Medium Set D Paper 2 · Question 12

A circle has centre $(h,k)$ and positive radius. Consider the statements

$P$ : Both $h$ and $k$ are rational.
$Q$ : The circle passes through at least three distinct points whose two coordinates are integers.

Which of the following correctly describes $P$ as a condition for $Q$ ?

P

is necessary but not sufficient for

Q

P

is both necessary and sufficient for

Q

P

is neither necessary nor sufficient for

Q

P

is sufficient but not necessary for

Q

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