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In this image, I need to find the center point of a tangent circle to two other circles with a known radius.

The information I can gather is: $rT$, $rA$, $rB$, $(Ax,Ay)$, $(Bx,By)$,

Not given is: $(TAx,TAy)$, $(TBx,TBy)$, $(Tx,Ty)$,

I searched for answers on this site, but couldn't find any before posting. Any insight would be much appreciated.

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    are you looking for $(Tx,Ty)$? – 2017-01-06
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    Yes, I am looking for (Tx,Ty) – 2017-04-05

1 Answers 1

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$(T_x,T_y)$ is a distance of $rT+rA$ from the center of $A.$

and $rT+rB$ from the center of $B.$

Solve this system of equations:

$(x-A_x)^2 + (y-A_y)^2 = (rT + rA)^2\\ (x-B_x)^2 + (y-B_y)^2 = (rT + rB)^2$

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    @RossMillikan Sorry, $T$ is $rT + rB$ from $B.$ (I had it correct in the algebra bellow.) – 2017-01-06
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    It is important to point out that the line between the centers of the circles goes through the tangent point. That justifies the claim that the distance between the centers of $A$ and $T$ is $rA+rT$ – 2017-01-06