How many circle can be draw to pass through two given points

Options

A. 1
B. 2
C. 0
D. as many as possible

Answer

To determine how many circles can be drawn that pass through two given points, let's go through the solution step by step.

### Step-by-Step Solution:

1. **Identify the Two Points**:
Let's denote the two points as A and B. These points can be anywhere on a plane.

**Hint**: Visualize or sketch the two points on a piece of paper to understand their positions.

2. **Understanding Circle Definition**:
A circle is defined as the set of all points that are equidistant from a fixed point (the center of the circle).

**Hint**: Remember that the distance from the center to any point on the circle is the radius.

3. **Drawing Circles Through Points A and B**:
To draw a circle that passes through both points A and B, we can choose any point as the center of the circle. The distance from this center to points A and B must be equal (the radius).

**Hint**: Think about how you can place the center of the circle anywhere along the perpendicular bisector of the line segment joining A and B.

4. **Infinite Possibilities**:
Since the center of the circle can be placed anywhere along the perpendicular bisector of the line segment AB, there are infinitely many positions for the center. Thus, we can draw infinitely many circles that pass through points A and B.

**Hint**: Visualize the perpendicular bisector as a line that cuts the segment AB in half at a right angle, allowing for an infinite number of centers along this line.

5. **Conclusion**:
Therefore, the answer to the question is that an infinite number of circles can be drawn through two given points A and B.

**Hint**: Remember that the concept of infinity means there is no limit to the number of circles you can draw in this scenario.

### Final Answer:
There are infinitely many circles that can be drawn to pass through two given points.