Circles with centers of \((2,2)\) and \((17,10)\) are both tangent to the x-axis. What is the distance between the closest points of the two circles?
The distance between the closest points will occur on the line segment that joins the two centers of the circles
The length of this segment is
√ [ (17 - 2)^2 + ( 10 - 2)^2 ] = √ [ 15^2 + 8^2] = √289 = 17 units
From this, we want to subtract the two radii of the circles, i.e., 2 and 10
So....the distance between the closest points = 17 - 2 - 10 = 17 - 12 = 5 units
Here's a pic :