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Two circles of radius 2 are tangent to each other and to a straight line. A third circle is placed so that it is tangent to both of the other circles and also tangent to the same straight line.
What is the radius of the third circle?
![[asy]
size(150);
draw((-1,0)--(3,0)); // ground line
draw(circle((0,1),1)); // left big circle
draw(circle((2,1),1)); // right big circle
draw(circle((1,0.25),0.25)); // small circle in between
[/asy]](//latex.artofproblemsolving.com/d/0/d/d0d9cb2706e9b913e2051e224b8e64537c7b8332.png)
What is the radius of the third circle?
![[asy]
size(150);
draw((-1,0)--(3,0)); // ground line
draw(circle((0,1),1)); // left big circle
draw(circle((2,1),1)); // right big circle
draw(circle((1,0.25),0.25)); // small circle in between
[/asy]](http://latex.artofproblemsolving.com/d/0/d/d0d9cb2706e9b913e2051e224b8e64537c7b8332.png)