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Re: In the xy-coordinate plane how many circles can be constructed that ha
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26 Aug 2019, 09:28
In the xy-coordinate plane how many circles can be constructed that have a center at (r, s), where r and s are integers, that have a radius with an integer length, and that in no portion lie outside the square region defined by 0≤x≤5 and 0≤y≤5?
The circle should lie within the the square defined by the region 0<=x<=5 & 0<=y<=5
The radius of the circle should be an integer, so the radius value could be 1 or 2
And the center (r, s) are integers, so we can construct circles with radius 1 at center (r, s) as = (1,1), (1,2), (1,3), (1,4), (2,1), (2,2), (2,3), (2,4), (3,1), (3,2), (3,3), (3,4), (4,1), (4,2), (4,3), (4,4) and with radius 2 and at center (r, s) as = (2,2), (2,3), (3,2), and (3,3)
So, the total number of circles is 20
Answer is (B)