Explanation
So we must find the center of the earthquake. We have three points and we know the distances from each of these points to the earthquake. In order to find the center we just need to make three circles, each centered in one of the three points and its radius must be the distance to the center of the earthquake. If we do this correctly then the three circles will meet in a given point D which is the center of the earthquake.
In order to draw a circle using the tool given by the question you'll need its center and a point in the circumference. So let's construct each of the circles:
First we have point A=(-15,2) which is at a distance of 13mi from the earthquake. So we must construct a circle centered around A with a radius of 13 units. Any point at a distance of 13 units from A will be useful, for example a point that has a horizontal distance of 13 units from A. We'll name this point E and we have:
[tex]E=(-15+13,2)=(-2,2)[/tex]
So the first circle is the one that passes through (-2,2) and is centered around (-15,2).
Now we repeat this process with the other circles. We have B=(-11,1) and its distance to the earthquake is 10 miles so we can add 10 to its x-value to find a point that is at a distance of 10 units from it:
[tex]F=(-11+10,1)=(-1,1)[/tex]
So this circle is centered around (-11,1) and it passes through (-1,1).
For the third circle we have C=(-6,3) and its distance to the earthquake is 5 miles. Then a point located at 5 miles from C could be:
[tex]G=(-6+5,3)=(-1,3)[/tex]
So the third circle is centered around (-6,3) and passes through (-1,3).
With all this information we can graph the three circles:
As you can see these three circles intercept each other at (-3,7). Then the earth quake is located at (-3,7).
Answer
The graphs are displayed in the picture above. The center of the earthquake is located at (-3,7).
