In the xy-coordinate plane how many circles can be constructed that ha

First of all, the square is of dimension 5x5 as 0 ≤ x ≤ 5 and 0 ≤ y ≤ 5 and centers of all circles have coordinates as integer values and so are lengths of radii of all the circles.

Now, circles can be of either radius 1 unit or 2 units only since radius of 3 would result in diameter of 6 units whereas as per question no portion of a circle should be outside the square of dimension 5 x 5.

Consider the snapshot as attached.

Here, points except purple color and those on x & y axis can only be centers of circles.
1. Blue points can have length of 1 unit only to suffice the condition. Total blue points = 12 i.e. total circles are 12x1 = 12.
2. Pink points can have length of 1 and 2 units to suffice the condition. Total pink points = 4 i.e. total circles are 4x2 = 8.

Hence total circles are 20.

Answer (B).