(i) A tangent to a circle is a line coplanar with the circle which meets the circle at exactly one point.

(ii) When two circles touch each other at exactly one point, either externally or internally, they are said to be tangent to each other.

AB is the common tangent to both the circles that are tangent to each other.

Based on the above information, how many common tangents do you think can be drawn for two circles, when the circles are as given below ? Draw the tangent(s) in each case.

(a)

The two circles touch each other externally at one point. Hence, 3 common tangents can be drawn — two direct common tangents and one common tangent at the point of contact.

(b)

The two circles lie apart and neither touch nor intersect. Hence, 4 common tangents can be drawn — two direct common tangents and two transverse common tangents.

(c)

The two circles touch each other internally at one point. Hence, 1 common tangent can be drawn, at the point of contact.

(d)

The two circles intersect each other at two points. Hence, 2 common tangents can be drawn — two direct common tangents.