From 11:00PM PDT on Friday, July 1 until 5:00AM PDT on Saturday, July 2, the Shmoop engineering elves will be making tweaks and improvements to the site. That means Shmoop will be unavailable for use during that time. Thanks for your patience!
We have changed our privacy policy. In addition, we use cookies on our website for various purposes. By continuing on our website, you consent to our use of cookies. You can learn about our practices by reading our privacy policy.
© 2016 Shmoop University, Inc. All rights reserved.
Circles

Circles

At a Glance - The Basics of Circles

Mathematicians like to define things before they start talking about them. This is a good idea in other areas of life too. Ever brought a cake pan to a baseball game because you heard there would be a batter?

Given a point O and a distance r, the circle with center O and radius r is the set of all points in a plane that are exactly r units away from O. Easy enough, right?

Example 1

Suppose the radius of ⊙O is 7 m and OP is 3 m. Is the point P in the exterior of ⊙O, in the interior of ⊙O, or on ⊙O?


Example 2

Suppose the radius of ⊙O is 10 km and OP is 10 km. Is the point P in the exterior of ⊙O, in the interior of ⊙O, or on ⊙O?


Example 3

Suppose the radius of ⊙O is 175 cm. OP is 213 cm. Is the point P in the exterior of ⊙O, in the interior of ⊙O, or on ⊙O?


Example 4

Suppose a circle is divided into six central angles of the same measure. What is the measure of one of them?


Exercise 1

Consider a circle with center O and radius 20 m. Is P such that OP = 8 m in the interior of the circle, in the exterior of the circle, or on the circle?


Exercise 2

Consider a circle with center O and radius 20 m. Is Q such that OQ = 30 cm in the interior of the circle, in the exterior of the circle, or on the circle?


Exercise 3

Consider a circle with center O and radius 20 m. Is S such that OS = 20 m in the interior of the circle, in the exterior of the circle, or on the circle?


Exercise 4

Consider a circle with center O and radius 20 m. Is O in the interior of the circle, in the exterior of the circle, or on the circle?


Exercise 5

Consider a circle with center O and radius 20 m. Is T such that OT = 100 m in the interior of the circle, in the exterior of the circle, or on the circle?


Exercise 6

Consider a circle with center O and radius 20 m. Is U such that OU > OS in the interior of the circle, in the exterior of the circle, or on the circle?


Exercise 7

Consider a circle with center O and radius 20 m. Is V such that OS < OV < OU in the interior of the circle, in the exterior of the circle, or on the circle?


Exercise 8

In the figure below, points A, B, C, and D are on ⊙O. If m∠BOC = 50°, m∠COD = 140°, and m∠DOA = 65°, what is m∠AOB?


Exercise 9

In the figure below, suppose now that m∠BOC = 67° instead of 50°. How does the measure of m∠AOB change?


People who Shmooped this also Shmooped...

Advertisement