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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?

 Jul 16, 2019
 #1
avatar+105195 
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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 : 

 

 

cool cool cool

 Jul 16, 2019

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