Question 328517
{{{drawing(300,300,-10,10,-10,10,circle(-3,0,.2),circle(6,0,.2),line(-1.1,4.5,-1.1,-4.5),blue(line(-3,0,6,0)),locate(-1.3,6,V),locate(-1.3,-5.5,W),
green(line(6,0,-1.1,4.5)),green(line(-1.1,4.5,-3,0)),
locate(-4,3,10),locate(3,3,17),locate(-2,0,a),locate(2.3,0,b),locate(-0.5,2,8),
circle(-3,0,5),circle(6,0,8.5))}}}
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As you can see from the figure, a-8-10 and b-8-17 form right triangles.
Use the Pythagorean theorem to solve for {{{a}}} and {{{b}}}.
{{{a^2+8^2=10^2}}}
{{{a^2=100-64}}}
{{{a=6}}}
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{{{b^2+8^2=17^2}}}
{{{b^2=289-64}}}
{{{b=15}}}
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Let {{{D}}} be the distance between the circle centers.
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{{{D=a+b}}}
{{{highlight(D=21)}}}