Practice Circles in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

The set of all points in a plane at a fixed distance (the radius) from a central point called the center.

Spin around with your arm fully outstretchedβ€”your fingertip traces a perfect circle.

Showing a random 20 of 50 problems.

Example 1

medium
If you double a circle's radius, what happens to its circumference?

Example 2

challenge
Four identical coins of radius 11 are packed snugly in a square so each touches two neighbors. Find the area of the gap in the center between the four coins.

Example 3

easy
Using Ο€β‰ˆ3.14\pi \approx 3.14, estimate the circumference of a circle with diameter 1010.

Example 4

medium
A chord of length 1616 is 66 from the center. Find the radius.

Example 5

medium
What is a tangent line to a circle?

Example 6

challenge
A circle is inscribed in a regular hexagon of side 44. Find the circle's radius.

Example 7

medium
Two circles have radii 33 and 66. What is the ratio of their areas?

Example 8

challenge
Explain why, if a circle's circumference equals its area numerically, the radius must be 22.

Example 9

easy
A circular pizza has radius 77 inches. Use Ο€β‰ˆ3.14\pi\approx 3.14 to estimate its circumference.

Example 10

easy
A circle has diameter 2626. What is its radius?

Example 11

easy
A circle has a diameter of 2020 cm. What is its radius?

Example 12

hard
Three circles of radius 11 are arranged so each touches the other two. Find the side length of the equilateral triangle joining centers.

Example 13

challenge
A goat is tied by a 77-meter rope to a corner on the outside of a square barn with side 1010 meters. Over what area can the goat graze?

Example 14

medium
A square has side 1010. Find the radius of the circumscribed circle (passing through all 44 corners).

Example 15

easy
A circle has radius 66. Find its area in terms of Ο€\pi.

Example 16

easy
A circle has radius 88. Find its circumference in terms of Ο€\pi.

Example 17

easy
A circle has radius 33. Write its circumference in terms of Ο€\pi.

Example 18

easy
Which is longer in a given circle: a radius or a diameter?

Example 19

hard
A circle has center (2,3)(2,3) and passes through (5,7)(5,7). Find its radius.

Example 20

hard
A circle has equation (xβˆ’3)2+(y+2)2=16(x-3)^2+(y+2)^2=16. State its center and radius.