Point P lies in plane M. How many circles are there in plane M that have center P and a circumference of 6ㅠ inches?
a) none
b) one
c) two
d) four
e) more than four
To determine how many circles in plane M have center P and a circumference of 6π inches, we need to understand the properties of a circle.
A circle is defined by its center and radius. The circumference of a circle is given by the formula C = 2πr, where C is the circumference and r is the radius. We are given that the circumference is 6π inches, so we can equate this to the formula:
6π = 2πr
Dividing both sides of the equation by 2π, we get:
r = 3 inches
Now that we know the radius of the circle, we can determine the number of circles in plane M with center P and a circumference of 6π inches.
A circle is defined by its center, so any point in plane M can be the center of a circle. Therefore, there are infinitely many points in plane M that can serve as the center of a circle with the given properties.
The answer is: e) more than four (infinitely many) circles