Module Overview
Circles

Time lapse photo of starts moving in a circular pattern throughout the night sky

A circle is a two-dimensional figure comprised of the points equidistant from a fixed point. In this module, you will apply your knowledge of prior geometry concepts to solve problems dealing with circles. This knowledge includes circumference, area of a circle, the distance and midpoint formula, and coordinate geometry. Your study will begin by exploring the angles formed by intersections in the interior and exterior of a circle. You will also investigate central and inscribed angles, lengths of segments, arc lengths, sector areas, and the equation of a circle. Of course, no study of circles is complete without applying your newly gained knowledge to practical problems.

Getting Started

a compass and two pencils on a black desk Getting started iconCircles with the same center in the same plane but with different radii are called concentric circles. Before you begin your exploration of circles, create a mobile of concentric circles. The only materials you need are a compass, paper, a 12-inch piece of string, and a pair of scissors.

To get started, place the compass in the center of a sheet of paper. Draw a small circle. Next, without moving the compass from the center, draw nine different size circles. Cut around the edge of each circle to make nine rings. Place five of the rings inside one another. Next, connect the circles with a 12-inch piece of string. Lastly, decorate your concentric circles mobile in a creative and unique way.

Snap a photo of your concentric circles mobile and post it to the discussion board. Then, return to the topic discussion several times over the next few days to read your coursemates’ posts. Vote for the three mobiles that you think are most creative by replying to each with the word “like” and writing at least one sentence explaining why you like it. The mobile with the most “likes” is the class favorite.

Key Vocabulary

Glossary iconTo view the definitions for these key vocabulary terms, visit the course glossary.

arc
arc length
central angle
chord
circumference
circumscribed circle
diameter
equation of a circle
inscribed angle
inscribed circle
intercepted arc
point of tangency
radius
secant
sector
sector area
semicircle
tangent