Final answer:
To find the radius of a circle with two points directly across from each other on the circle, measure the distance between them and divide by two. If the two points are not directly across, more complex geometric methods are required, and knowing just two points is insufficient without additional information.
Step-by-step explanation:
To find the radius of a circle when given two points on the circumference, one would typically need the center of the circle as well. However, if the two points are at opposite ends of a diameter, the radius is half the distance between them. Assuming we have the diameter, the process would involve measuring the distance between the two points, dividing by two, and concluding that's the circle's radius. If you have just any two points and no further information, additional steps involving the construction of perpendicular bisectors or other geometric principles might be required to find the circle's center and then its radius.
For example, the ancient Greeks knew the relationship between a circle's circumference and its radius is 2πr where π (pi) is approximately 3.14159. Thus, to find the radius, one could rearrange this formula if the circumference is known. On the other hand, when considering the area of a circle, one must use the formula A = πr². Knowing the area allows us to solve for r by taking the square root of the area divided by π.