A circle tangent to two circles
Problem
Circles with centres $O_1$ and $O_2$ and radii $r_1$ and $r_2$ both touch, externally, a third circle with centre $O$ and radius $r$. Writing $d_1 = OO_1$ and $d_2 = OO_2$, prove that $d_1 - d_2 = r_1 - r_2$.
The diagram
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