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up vote 6 down vote favorite 1 Three circles of different radii are tangent to each other externally. The distance between their centers are $9 cm$, $8 cm$, and $11 cm$. Find the radius of each circle. Find the area in between the three circles. The distance between the centers of two tangent circles should be the sum of their radii. If we call the radii $r_1,r_2,r_3$ then we get a system of equations $$begin{align}r_1+r_2&=9\r_2+r_3&=8\r_3+r_1&=11end{align}$$ From this we can find $r_1,r_2,r_3$. Let us call $O_1,O_2,O_3$ the centers of the circles. For the area between the centers we could compute it as the difference of the area of the triangle $O_1O_2O_3$ minus the three circular sectors that the circles cover. We have the area of the triangle because we have its sides $9,8,11$ and we could use Heron