Can you visualise it?
Geometry
Level
3
Number of integral points contained within the circle .
The answer is 109.
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1 solution
At y={0,1,2,3}, the 11 points x={-5, -4, ... , 5} lie within the circle.
At y=4, the 9 points x={-4,...,4} lie within.
At y=5, the 7 points x={-3,...,3} are included.
The included points are symmetric about y=0, so the total number of integral points within the circle is
11 + 2 (7+9+3 11) = 11 + 2*49 = 109.