Direct Common Tangents

A common tangent is called a direct common tangent if both the circles lie on the same side of it.

The figures given below shows common tangents in three different cases, that is when the circles are apart, as in (i);

$Direct Common Tangents when the Circles are Apart$

when they are touching each other as in (ii);

$Direct Common Tangents when the Circles are touching each other$

and when they are intersecting each other as in (iii).

$Direct Common Tangents when the Circles are Intersecting each other$

In each case, WX is a direct common tangent as both the circles lie below it. YZ is the other direct common tangent as both the circles lie above it.

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