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I have two circles with the same radius and I want to calculate the points of tangency.

For example, in the picture below, I want to calculate $(x_3, y_3)$ and $(x_4,y_4)$. I have the radius and the distance between the two circles as shown below:

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    $A$ tangent and a radius to a circle at any point are perpendicular. You might find that fact helpful.2012-07-14

2 Answers 2

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The gradient of the tangent to any circle is given by $-\frac{(x'-a)}{(y'-b)}$ Where (x',y') is the point of tangency and (a,b) is the center of the circle. Now the gradient of the line joining the centers of the two circles is same as the gradient of the tangent. Hence in this case this essentially translates to the following equation $ -\frac{(x_3-x_1)}{(y_3-y_1)}=\frac{(y_2-y_1)}{(x_2-x_1)}$ The other equation is $ (x_3-x_1)^2+(y_3-y_1)^2= R^2$ Solving the above two equations you will get two points for $(x_3,y_3)$. This shows the existence of two parallel tangents. Similarly you can solve for $(x_4,y_4)$

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    you are very welcome!2012-07-16
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\begin{eqnarray} y_3 = y_1 + R \cos \theta \\ x_3= x_1 + R \sin \theta \\ y_4= y_2 +R \cos \theta \\ x_4 = x_2 +R \sin \theta \\ \end{eqnarray}

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    no,i dont have Length of tangent line2012-07-14