The number of tangents that can be drawn to two non-intersecting circles is

Options

A. 4
B. 3
C. 2
D. 1

Answer

To determine the number of tangents that can be drawn to two non-intersecting circles, we can follow these steps:

### Step 1: Understand the Configuration of the Circles
We have two non-intersecting circles. This means that they do not touch or cross each other.

**Hint:** Visualize the two circles as separate entities on a plane, ensuring that they do not overlap.

### Step 2: Identify the Types of Tangents
For two circles, there are two types of tangents:
1. **External Tangents:** These tangents touch both circles from outside.
2. **Internal Tangents:** These tangents pass between the circles and touch each circle from the inside.

**Hint:** Remember that external tangents will not cross the line segment connecting the centers of the circles, while internal tangents will.

### Step 3: Count the Tangents
For two non-intersecting circles:
- There are **2 external tangents**.
- There are **2 internal tangents**.

So, the total number of tangents that can be drawn to the two circles is:
\[ \text{Total Tangents} = \text{External Tangents} + \text{Internal Tangents} = 2 + 2 = 4 \]

**Hint:** When counting, ensure you consider both external and internal tangents separately.

### Step 4: Conclusion
Thus, the total number of tangents that can be drawn to two non-intersecting circles is **4**.

**Final Answer:** 4 tangents can be drawn to two non-intersecting circles.