Introduction to Circle Theorems
Circle theorems describe the relationships between angles, chords, tangents, and arcs in circles. Learning the key parts of a circle is the foundation for understanding these theorems.
What You Need to Know
Key Concept Diagram
The radius connects the centre to any point on the circle; all radii are equal
A chord is a line segment joining two points on the circle; the diameter is the longest chord
The angle at the centre is twice the angle at the circumference subtending the same arc
Angles in the same segment (same side of a chord) are equal
Key Vocabulary
Radius
A line segment from the centre of a circle to its circumference
Chord
A line segment with both endpoints on the circle
Arc
A portion of the circumference of a circle
Subtend
To form an angle at a point by the two lines drawn to the endpoints of an arc or chord
Knowledge Check
Select the correct answer for each question. Click "Check Answer" to see if you are right.
Question 1
If the radius of a circle is 5 cm, what is the diameter?
Question 2
The angle at the centre subtended by an arc is 80deg. What is the angle at the circumference subtending the same arc?
Question 3
What do we call a chord that passes through the centre of a circle?
Key Concepts Summary
- ●The radius connects the centre to any point on the circle; all radii are equal
- ●A chord is a line segment joining two points on the circle; the diameter is the longest chord
- ●The angle at the centre is twice the angle at the circumference subtending the same arc
- ●Angles in the same segment (same side of a chord) are equal