Question

If two circles touch internally, then the number of their common tangents is

• A. 2
• B. 3
• C. 0
• D. 1

Answer 1

The Correct Option is D

When two circles touch internally, it means that one circle lies completely inside the other, and they share exactly one point of contact. In this case:

• The distance between the centers of the two circles is equal to the difference of their radii.
• No external tangents can be drawn because one circle is entirely inside the other.
• Only one direct common tangent exists, which passes through the single point of contact between the two circles.

For two circles that touch internally, there is exactly one common tangent, which is the tangent at their point of contact.

Final Answer: The number of common tangents is \( \mathbf{1} \).