If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

Main content

Circles FAQ

Frequently asked questions about circles

Why do we need to learn about circles?

There are many places where we use properties of circles in the real world. For example, architects often use arcs and sectors when designing buildings, and engineers use circles when designing gears and other mechanical parts. Additionally, understanding the properties of circles can help us solve problems in geometry, trigonometry, and calculus.

What's the difference between a radius and a diameter?

The radius of a circle is the distance from the center of the circle to any point on the circle. The diameter is twice the radius, or the distance across the circle through the center.

What are tangent and secant lines?

A tangent line is a line that touches a circle at just one point. A secant line is a line that cuts through a circle at two points.

What are radians?

Radians are a unit of measurement for angles.
One radian is the angle measure that we turn to travel one radius length around the circumference of a circle.
We often use radians in geometry because they make working certain formulas easier.

What is arc length?

Arc length is the distance along a curved line, like on the edge of a circle.
On a circle, we need to know the central angle of the arc (θ) and the radius of the circle (r) to find arc length.
If θ is in degrees:
arc length=θ360°2πr
If θ is in radians:
arc length=θr

What is a sector?

A sector is a part of a circle, defined by two radii (the plural of radius) and the arc between them. Think of it as "pie slice" of the circle.

How do we find the area of a sector?

We need to know the central angle of the sector (θ) and the radius of the circle (r) to find the sector's area.
If θ is in degrees:
areasector=θ360°πr2
If θ is in radians:
areasector=θ2ππr2
Note that we could simplify the formula that uses radians a bit:
areasector=12θr2

What's an inscribed angle?

An inscribed angle is an angle that has its vertex on the circumference of a circle.

What is an inscribed shape?

An inscribed shape is a shape that is drawn inside a circle such that all of its vertices are touching the circumference of the circle.

Want to join the conversation?

  • duskpin ultimate style avatar for user Zane
    I have some troubles on word problems. Any tips?
    (7 votes)
    Default Khan Academy avatar avatar for user
    • blobby blue style avatar for user joshua
      I'm not good at math but here's some methods that I use when tackling word problems.

      - Try to visualize the problem. Drawing out the problem statement tends to help you have a better grasp on it is trying to ask you.

      - Write down every equation that you find. If you don't know the value of an object, simply let a variable to denote that unknown. This will let you have a (kinda) direction of what you will be trying to find.
      For example if the problem states that "between two objects one is faster than another by 100 mph", you simply let one object's speed be A mph, another be B mph, and define A < B. Now you can write down A + 100 = B.
      After you think you have written down all possible useful equations, go ahead and attempt connecting equations. But what formula to apply after this step requires you to be extremely familiar with all formulas (At least for the topic you are doing).

      Note that this is my accumulated experience after doing a lot of problems. You should find a suitable way for you to solve problem comfortably, even if it means a lot of struggling.

      Hope this helps.
      (8 votes)
  • aqualine ultimate style avatar for user Meryke Varmheldt
    Does anyone else have trouble/tips with the area of a sector?
    (6 votes)
    Default Khan Academy avatar avatar for user
  • leaf red style avatar for user Algirdas Varnagiris
    Why is there no practice for drawing ? You showed videos, but didn't let us practice...
    (5 votes)
    Default Khan Academy avatar avatar for user
  • blobby green style avatar for user marc
    what is the FAQ meaning
    (2 votes)
    Default Khan Academy avatar avatar for user
  • male robot hal style avatar for user inocenciojamilbenito
    why topics about secants not covered alot i this unit?
    (1 vote)
    Default Khan Academy avatar avatar for user