[Mutual Position of Two Circles]

What is the mutual position of two circles if:

a) the distance between the centers is 10, and the radii are 8 and 2;

b) the distance between the centers is 4, and the radii are 11 and 17;

c) the distance between the centers is 12, and the radii are 5 and 3?
Let $O_{1}$ and $O_{2}$ be the centers of the circles, $R$ and $r$ be their radii, and $R \geqslant r$.

If $R+r=O_{1} O_{2}$, then the circles touch.

If $R+r<O_{1} O_{2}$, then one circle is located outside the other.

If $O_{1} O_{2}<R-r$, then one circle is located inside the other.

## Answer

a) touch; b) one inside the other; c) one outside the other.