To solve the problem of finding the radius of the given circle, we should first identify the center of the circle and then determine the distance from the center to any point on the circumference, which is the radius.

Step-by-Step Solution:

1. Identifying the Center: The center of the circle is labeled as point $C(3, 1)$.

2. Using Point $P$ to Find the Radius: The point $P$ is on the circumference of the circle, and the distance $PC = 5$. Since $PC$ is a radius of the circle, the radius of the circle is equal to 5.

Thus, the radius of the given circle is 5.

Conclusion:

The correct answer is:

• Option 4: 5

Would you like a more detailed explanation of any part of the solution?

Here are some related questions you might find interesting:

1. How do you calculate the distance between two points in a coordinate plane?
2. What is the formula for the equation of a circle given its center and radius?
3. How can you determine if a point lies inside, outside, or on a circle?
4. What are the properties of a circle's radius and diameter?
5. How do you find the midpoint between two points in a coordinate plane?

Tip: To find the radius of a circle, you only need the center and a point on the circumference. Use the distance formula to calculate the radius directly!