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You join the centres of the two circles. Divide this line in the ratio of the two radii. Draw the tangent from this point to either circle and extend it to touch the other circle.

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Q: How do you make transverse common tangent to two circles?
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If there are two nonoverlapping nonintersecting circles in a plane four lines can be tangent to both circles at the same time How could the circles be arranged so that there are 3 or 2 or 1 or 0 li?

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