Circles Examples in Math
Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Circles.
This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.
Concept 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 outstretched—your fingertip traces a perfect circle.
Read the full concept explanation →How to Use These Examples
- Read the first worked example with the solution open so the structure is clear.
- Try the practice problems before revealing each solution.
- Use the related concepts and background knowledge badges if you feel stuck.
What to Focus On
Core idea: Circles are defined by equidistance—every point is the same distance from center.
Common stuck point: Diameter = 2 \times radius. Area uses \pi r^2; circumference uses 2\pi r—do not mix them up.
Sense of Study hint: Draw a line from the center to the edge (radius), then draw a line all the way across through the center (diameter). Compare the two lengths.
Worked Examples
Example 1
easySolution
- 1 Key circle relationships: the diameter d spans the full width through the centre, so d = 2r. The radius r is the distance from centre to any point on the circle, so r = \frac{d}{2}.
- 2 Substitute r = 7 cm into d = 2r: d = 2(7) = 14 cm.
- 3 Verify the relationship: r = \frac{d}{2} = \frac{14}{2} = 7 cm ✓. The diameter is always exactly twice the radius regardless of the circle's size.
Answer
Example 2
mediumPractice Problems
Try these problems on your own first, then open the solution to compare your method.
Example 1
easyExample 2
easyRelated Concepts
Background Knowledge
These ideas may be useful before you work through the harder examples.