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 outstretched—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 1 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 π≈3.14, estimate the circumference of a circle with diameter 10.Diameter
Example 4
medium
A chord of length 16 is 6 from the center. Find the radius.Chord = 16, distance from center = 6 — 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 4. Find the circle's radius.
Example 7
medium
Two circles have radii 3 and 6. 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 2.
Example 9
easy
A circular pizza has radius 7 inches. Use π≈3.14 to estimate its circumference.
Example 10
easy
A circle has diameter 26. What is its radius?Diameter
Example 11
easy
A circle has a diameter of 20 cm. What is its radius?Diameter
Example 12
hard
Three circles of radius 1 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 7-meter rope to a corner on the outside of a square barn with side 10 meters. Over what area can the goat graze?
Example 14
medium
A square has side 10. Find the radius of the circumscribed circle (passing through all 4 corners).
Example 15
easy
A circle has radius 6. Find its area in terms of π.Radius
Example 16
easy
A circle has radius 8. Find its circumference in terms of π.Radius
Example 17
easy
A circle has radius 3. Write its circumference in terms of π.Radius
Example 18
easy
Which is longer in a given circle: a radius or a diameter?
Example 19
hard
A circle has center (2,3) and passes through (5,7). Find its radius.
Example 20
hard
A circle has equation (x−3)2+(y+2)2=16. State its center and radius.