Circumference and Arc Length

Two similar circles are shown. The circumference of the larger circle, with radius OB, is 3 times the circumference of the smaller circle, with radius OA. Radius OB measures x units. Which expression represents the circumference of the smaller circle with radius OA?

(2pi/3)x units

An arc on a circle measures 85°. The measure of the central angle, in radians, is within which range?

0 to pi/2 radians

Circle P has a circumference of approximately 75 inches. What is the approximate length of the radius, r? Use 3.14 for pi. Round to the nearest inch.

12 inches

Circle O has a circumference of approximately 250π ft. What is the approximate length of the diameter, d?

250 ft

In circle M, diameters JL and HK each measure 16 centimeters. What is the approximate length of minor arc JH? Round to the nearest tenth of a centimeter.

3.5 cm

In each circle below, a 50° angle with a vertex at the center of the circle is drawn. How are minor arc lengths CD and EF related?

The arc lengths are proportional: CD = 4EF

Since all circles are similar, a proportion can be set up using the circumference and diameter of each circle. Substitute the values d1 = 1, C1 = π, and d2 = 2r into the proportion. Which shows how to correctly solve for C2, the circumference of any circle with radius r?

a

Arc CD is 1/4 of the circumference of a circle. What is the radian measure of the central angle?

pi/2 radians

An arc on a circle measures 125°. The measure of the central angle, in radians, is within which range?

pi/2 to pi radians

In the diagram below, Θ is measured in radians. Which equation represents the relationship between the radius, r, and arc length, s?

s = Θ · r