Question

Find the diameter of this circle.

A.
`2√(10)`
B.
`4√(10)`
C. 8
D.
`2√(34)`

Answer 1

Check the picture below.

so we know the circle has that center and passes through (2 , -2), let's find its radius, keeping in mind that diameter = 2 * radius.

`~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{2}~,~\stackrel{y_1}{-2})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{-3})\qquad \qquad d = √(( x_2- x_1)^2 + ( y_2- y_1)^2) \\\\\\ \stackrel{radius}{r}=√((~~5 - 2~~)^2 + (~~-3 - (-2)~~)^2) \implies r=√((5 -2)^2 + (-3 +2)^2) \\\\\\ r=√(( 3 )^2 + ( -1 )^2) \implies r=√( 9 + 1 ) \implies r=√( 10 )~\hfill \underset{diameter}{\stackrel{(2)(r)}{2√(10)}}`

Answer 2

A

Explanation:

From looking at the graph, you can see that the center point of the circle is at (5, -3), so to figure out the diameter, you need to find the distance of that line ( y = - 3 ) that the circle is on. The diameter is about 6 point something which in the square root form can be represented by √36.

After knowing the diameter is about 6, choice C can be eliminated.

2√10 = √40

4√10 = √160

2√34 = √136

After expanding the square root, we can know that the closest option is A.