Answer:
[tex]D=14.56[/tex]
Step-by-step explanation:
We know that the diameter of a circle is twice the radius.
Calculate the radius of the circle with the formula for calculate the distance between two points:
[tex]d=r=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Where "r" is the radius.
Knowing that the center of the circle is at point (3, 1) and the circle passes through the point (1, -6), we can substitute values into the formula to find the radius:
[tex]r=\sqrt{(3-1)^2+(1-(-6))^2}=\sqrt{53}[/tex]
Then the diameter of the circle is:
[tex]D=2r\\D=2\sqrt{53}[/tex]
[tex]D=14.56[/tex]
