Chapter 9, Problem 6CT

Solution

To find: is it possible to draw two circles so that no common tangent can be drawn.

Yes, it is possible.

Concept Used:

Definition:

Tangent: It is a line which lies in the same plane as the circle O and intersects the circle at only one point.

Explanation:

Yes, it is possible to draw two circles so that no common tangent can be drawn.

Consider the figure below:

Here one circle is completely inside the other circle.

Now, any tangent drawn to the bigger circle will never intersect the smaller circle, so it can’t be tangent of the smaller circle.

And any tangent drawn to the smaller circle will intersect the bigger circle at two points, so it can’t be tangent of the bigger circle.

Hence, in this case both circles have no common tangents.