Circles: Parts and Terms
A circle is every point at a fixed distance from the center.
About this topic
A circle is the set of all points at a fixed distance, the radius, from the centre. Key terms: a diameter passes through the centre and equals twice the radius, a chord joins two points on the circle, a secant is a line cutting through it, a tangent touches it at exactly one point, and an arc is a piece of the circumference.
A tangent is perpendicular to the radius at the point of contact. These definitions are the vocabulary for every circle theorem and formula.
Worked example: a circle has radius 7, so its diameter is 14. A chord of length 10 sits at some distance from the centre, while the longest chord is the diameter itself. A tangent line touches only at one point, and the radius to that point forms a 90° angle with it. If a tangent is drawn from a point 13 away from the centre of a circle of radius 5, its length is √(169 − 25) = 12.
Wheels, clocks, lenses and orbits all rely on circles. Terms get mixed up often: a chord stays inside the circle, while a secant extends past it in both directions. The word radius means a segment from the centre, so every radius of a circle has the same length, but chords differ. Remember that the diameter is the longest chord. Label diagrams with the correct term before applying any formula and read the question carefully for radius versus diameter.
Key ideas
- Radius, diameter, chord, arc
- Diameter = 2 × radius
- π = circumference ÷ diameter
Quick check
Use cases: where Circles: Parts and Terms helps
- Homework: review the key idea behind Circles: Parts and Terms before you start a problem set.
- Exam revision: use the quick check to test whether you can recall Circles: Parts and Terms without notes.
- Visual learning: play with the interactive lab to see how Circles: Parts and Terms changes when you adjust its inputs.
- Teaching a friend: explain Circles: Parts and Terms in your own words, then compare your version with the key ideas.
Number and algebra skills are used in science, engineering, budgeting and computing.
Frequently asked questions
What is Circles: Parts and Terms?
A circle is every point at a fixed distance from the center.
What will I learn in Circles: Parts and Terms?
Radius, diameter, chord, arc. Diameter = 2 × radius. π = circumference ÷ diameter.
Is Circles: Parts and Terms part of Mathematics?
Yes. It is one of 200 Mathematics topics on LearnViz HighSchoolEdu, with 3 key ideas, a live animation and a quick check.
Does the Circles: Parts and Terms lab work on a phone or tablet?
Yes. The animation resizes to fit your screen and supports touch, so you can drag, tap and slide with your finger.
How should I study Circles: Parts and Terms?
Read the summary and key ideas first, play with the interactive lab to see the idea in motion, then answer the quick check. If you get a question wrong, go back to the key idea it tests.
Do I need an account, and is my progress saved?
No account is needed. Marking a topic as learned is saved in your own browser, so it stays on that device and is not sent to a server.