On the xy-plane, the center of the circle O is at the point (3,2). If the point (10, 2) lies outside of the circle and the point (3, 8) lies inside of the circle, which of the following could be the radius of the circle?

a. 5
b. 5.5
c. 6
d. 6.5
e. 7

Question

On the xy-plane, the center of the circle O is at the point (3,2). If the point (10, 2) lies outside of the circle and the point (3, 8) lies inside of the circle, which of the following could be the radius of the circle? 

a. 5
b. 5.5
c. 6
d. 6.5
e. 7

hybrik · Answer

Find the distance between (3,2) and (10,2) using the distance formula ( http://www.mathwarehouse.com/calculators/distance-formula-calculator.php) . Using the formula you find the distance of those two points is 7. And the radius can not be seven since 10,2 is out of the circle. You can eliminate E. Then, find the distance between (3,2) and (3,8). The distance is 6. So the radius has to be 6 because (3,8 ) is in the circle [C]