Question

what is the radius of this circle?

Explanation:

Step1: Identify the center of the circle

The center of the circle is at the point \((2, 2)\) (from the coordinate grid, the blue dot is at \(x = 2\), \(y = 2\)).

Step2: Find a point on the circle

Let's take a point on the circle, for example, the topmost point. From the grid, the topmost point seems to be at \((2, 8)\) (since the center is at \((2, 2)\) and moving up along the vertical line \(x = 2\)).

Step3: Calculate the distance between the center and the point on the circle (radius)

Using the distance formula between two points \((x_1, y_1)\) and \((x_2, y_2)\) which is \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). Here, \(x_1 = 2\), \(y_1 = 2\), \(x_2 = 2\), \(y_2 = 8\).
So, \(d=\sqrt{(2 - 2)^2+(8 - 2)^2}=\sqrt{0 + 36}=\sqrt{36} = 6\).
Alternatively, since the points are vertically aligned (same \(x\)-coordinate), we can just find the difference in \(y\)-coordinates: \(8 - 2=6\).

Answer:

The radius of the circle is \(6\).