Question 108743
I think the graph shows your problem.
{{{drawing( 300, 300, -10, 10, -10, 10,circle( 0, 0, 9 ),green(line( 0,0,0,5)),green(line( -7.483,5,0,5)),
locate(.5,3,5),
locate(-1.2,6.5,3*2+R),
locate(3,2,R),
locate(-3.3,2,R),
green(line(7.483,5,0,0)),
green(line(-7.483,5,0,0)),
green(line(7.483,5,0,5)))}}}
You form a right triangle with sides 5 and (6+R)/2, and a hypotenuse of R.
Using the Pythagorean theorem,
{{{((6+R)/2)^2+5^2=R^2}}}
{{{(R^2+12R+36)/4+25=R^2}}}Expand the square.
{{{(R^2+12R+36)+100=4R^2}}}Multiply both sides by 4.
{{{3R^2-12R-136=0}}} Group all terms on one side.
{{{R = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{R = (-(-12) +- sqrt( (-12)^2-4*3*(-136) ))/(2*3) }}}  
{{{R = ((12) +- sqrt( (144+1632)))/(6) }}}  
{{{R = ((12) +- sqrt( (1776)))/(6) }}} 
{{{R = ((12) +- 42.14)/(6) }}} 
{{{R = ((12) + 42.14)/(6) }}} Use only positive root, negative radius does not make sense in this application. 
{{{highlight(R=9.02)}}}
Check your answer.
{{{((6+R)/2)^2+5^2=R^2}}}
{{{((6+9.02)/2)^2+5^2=(9.02)^2}}}
{{{(7.51)^2+5^2=(9.02)^2}}}
{{{56.4+25=81.4}}}
{{{81.4=81.4}}}
True statement.
Good answer.
R=9.02 cm.