Question

the center of a circle is (7, 13) and the point (9, 17) is on the circle. what is the radius of the circle? radius = enter your next step here

Explanation:

Step1: Use distance formula

The radius is the distance between center \((7,13)\) and point \((9,17)\). The distance formula is \(d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\).

Step2: Calculate differences

\(x_2-x_1 = 9-7 = 2\), \(y_2-y_1 = 17-13 = 4\).

Step3: Compute squared differences

\(2^2 = 4\), \(4^2 = 16\). Sum: \(4 + 16 = 20\).

Step4: Find square root

Radius \(= \sqrt{20} = 2\sqrt{5}\) (or approx 4.47).

Answer:

\(2\sqrt{5}\) (or approximately 4.47)