In the xy-plane the point (-2 -3) is the centre of a circle, the point (-2, 1) lies inside the circle and the point (4, -3) lies outside the circle. If the radius r of the circle r is an integer then diameter ? Choose the most appropriate option
A) 6
B) 10
C) 4
D) 3
E) 2
Can be solved without much calculations.   You are given that (-2,-3) is the center of the circle. Point (4,-3) lies inside the circle ---&gt; the radius is lesser than distance of (-2,-3) from (4,-3) ---&gt; lesser than 6 units but the radius will also be greater than the distance of (-2,-3) from (-2,1) ----&gt; greater than 4 units.   Thus the radius is &gt;4 but &lt;6 and as it is an integer, the only possible value of radius = 5 units.   Diameter =2r= 10   10 is the correct answer.
<result>B</result>
In the xy-plane the point (-2 -3) is the centre of a circle, the point (-2, 1) lies inside the circle and the point (4, -3) lies outside the circle. If the radius r of the circle r is an integer then diameter ?