Circle Geometry
Circle geometry explores the special properties of angles, chords, and tangents in circles. These properties underpin advanced geometry and are used in engineering and design.
What You Need to Know
Key Concept Diagram
The angle at the centre is twice the angle at the circumference subtended by the same arc
Angles in the same segment of a circle are equal
The angle in a semicircle is always 90 degrees
A tangent to a circle is perpendicular to the radius at the point of contact
Key Vocabulary
Chord
A straight line joining two points on a circle
Arc
A portion of the circumference of a circle
Tangent
A line that touches a circle at exactly one point
Subtend
An angle is subtended by an arc when the arc lies between the angle's arms
Knowledge Check
Select the correct answer for each question. Click "Check Answer" to see if you are right.
Question 1
An arc subtends an angle of 70 degrees at the centre. What angle does it subtend at the circumference?
Question 2
What is the angle in a semicircle?
Question 3
A tangent meets a radius at the point of contact. What is the angle between them?
Key Concepts Summary
- ●The angle at the centre is twice the angle at the circumference subtended by the same arc
- ●Angles in the same segment of a circle are equal
- ●The angle in a semicircle is always 90 degrees
- ●A tangent to a circle is perpendicular to the radius at the point of contact