Assuming I only know the coordinates of the circle centers $A$ and $B$, and the three radii $R_A$, $R_B$ and $R_C$, how can I find the coordinates of the third circle center $C$?
2026-05-05 10:13:42.1777976022
Three tangent circles
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Hint
If you call $C(x,y)$ then:
$$(x-x_A)^2+(y-y_A)^2=(R_A+R_C)^2$$
$$(x-x_B)^2+(y-y_B)^2=(R_B+R_C)^2$$
Solve the system and get $C$.
You will find two solutions.
Can you see why that happens? Can you finish?