Question

what is the radius of this circle?

Explanation:

Step1: Identify the center and a point on the circle

The center of the circle is at \((7, 0)\) (from the graph, the purple dot) and a point on the circle is at \((10, 0)\) (where the circle intersects the x - axis on the right).

Step2: Calculate the distance between the center and the point (radius)

The distance formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). Since \(y_1 = y_2=0\) (both points are on the x - axis), the formula simplifies to \(d=\vert x_2 - x_1\vert\).
Substitute \(x_1 = 7\) and \(x_2 = 10\) into the formula: \(d=\vert10 - 7\vert=3\). Also, we can check with the left - most point of the circle \((4,0)\), the distance from \((7,0)\) to \((4,0)\) is \(\vert7 - 4\vert = 3\).

Answer:

The radius of the circle is 3.