Question

1. the center of a circle is (13, 18) and the point (3, 12) is on the circle. what is the radius of the circle? radius = enter your next step here

Explanation:

Step1: Use distance formula for radius

The radius is the distance between center \((13,18)\) and point \((3,12)\) on the circle. Distance formula: \(d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\)

Step2: Substitute coordinates into formula

\(d = \sqrt{(3 - 13)^2 + (12 - 18)^2} = \sqrt{(-10)^2 + (-6)^2}\)

Step3: Calculate the value inside the square root

\(\sqrt{100 + 36} = \sqrt{136}\)

Step4: Simplify the square root

\(\sqrt{136} = \sqrt{4 \times 34} = 2\sqrt{34}\) (or decimal approx \(11.66\))

Answer:

\(2\sqrt{34}\) (or approximately \(11.66\))