What is the maximum number of common tangents which can be drawn to the circle, if the distance between the circles is equal to the sum of their radii?

Options

A. 0
B. 1
C. 3
D. 4

Answer

To determine the maximum number of common tangents that can be drawn to two circles when the distance between the centers of the circles is equal to the sum of their radii, we can follow these steps:

### Step 1: Understand the Configuration of the Circles
When the distance between the centers of the two circles is equal to the sum of their radii, it means that the circles are externally tangent to each other. This configuration occurs when the two circles touch at exactly one point.

### Step 2: Identify the Types of Tangents
For two circles, there are generally four types of tangents:
1. Two external tangents
2. Two internal tangents

However, when the circles are externally tangent, the internal tangents cannot be drawn because the circles do not overlap.

### Step 3: Count the Tangents
In the case of externally tangent circles:
- There are **2 external tangents** that can be drawn.
- There are **no internal tangents** since the circles do not overlap.

### Step 4: Conclusion
Thus, the maximum number of common tangents that can be drawn to the two circles when they are externally tangent is **2**.

### Final Answer
The maximum number of common tangents that can be drawn to the circles is **2**.

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