# distance between centers of two touching circles

Lets say we have two circles with radii 2 and 3 respectively.

If we then put Circle radius 2 on a flat surface, then the other circle on the flat surface so they touch once, what is the distance between the two centers?

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A the point of contact the circles share a mutual external tangent and so the two radii are both perpendicular to that line. Therefore the center to center distance is simply $r_1 + r_2$, in this case $2 + 3 = 5$.

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Clearly the question had been a homework question... –  Sasha Aug 25 '12 at 18:40
but that tangent may not be perpendicular to the surface –  fosho Aug 25 '12 at 18:41
@fosho What do you mean? Since the circles lie on the same flat surface I assume that they are embedded in the same plane. In that case any tangent to the circle also lies in the same plane containing the circles. –  EuYu Aug 25 '12 at 18:55