+1206 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?
+128474 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 :
