Answer by David Quinn for Circle tangent to three tangent circles (without...
As you have observed, $AB$ and $AC$ are perpendicular, so take $A$ as the origin and assign coordinates $B(4,0)$ and $C(0,3)$.Let the centre of the inner circle be at $(a,b)$ and the radius is $r$....
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Circle tangent to three tangent circles (without the Soddy/Descartes formula)
We have three circles tangent to each other with radii $1$, $2$, and $3$. Another circle is tangent to the other circles; find the radius of that circle using elementary geometry, without the Soddy...
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