Question

what is the radius of this circle?

Explanation:

Step1: Identify center and a point on the circle

The center of the circle is at \((0, 6)\) (from the graph, the yellow dot). A point on the circle is \((0, 10)\) (topmost point on the circle along the y - axis).

Step2: Calculate the distance between center and the point

The distance formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). Here, \(x_1 = 0,y_1 = 6,x_2 = 0,y_2 = 10\). So \(d=\sqrt{(0 - 0)^2+(10 - 6)^2}=\sqrt{0 + 16}=4\). Since the distance from the center to a point on the circle is the radius, the radius \(r = 4\).

Answer:

4