Question

The number of common tangents of two intersecting circles is

• A. 1
• B. 2
• C. 3
• D. infinitely many

Hint:

Remember the number of common tangents for different circle positions: - Circles are separate: 4 common tangents (2 direct, 2 transverse) - Circles touch externally: 3 common tangents (2 direct, 1 transverse) - Circles intersect: 2 common tangents (both direct) - Circles touch internally: 1 common tangent - One circle inside another: 0 common tangents

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
This question asks for the number of common tangents that can be drawn to two circles that intersect each other at two distinct points.

Step 2: Detailed Explanation:
Let's visualize the situation: When two circles intersect at two different points, they overlap partially.
- We can draw two tangents that are external to both circles. These are called direct common tangents.
- It is not possible to draw any transverse (or indirect) common tangents that would cross the space between the circles, because the circles themselves occupy that space.
Therefore, there are exactly two common tangents.

Step 3: Final Answer:
The number of common tangents of two intersecting circles is 2.