Circle geometry
Categories: gcse geometry circle geometry circle theorems
This section covers circles and circle geometry. This includes the parts of a circle, and all the circle theorems required for GCSE Maths or equivalent exams.
The circle theorems are a set of rules of circle geometry that allow us to find sides and angles related to circles in various different situations. The GCSE curriculum, at the time of writing, covers seven circle theorems:
- Perpendicular bisector of a chord
- Angle at the centre of a circle is twice the angle at the circumference
- Angle in a semicircle is 90°
- Angles in the same segment of a circle are equal
- Opposite angles in a cyclic quadrilateral add up to 180°
- The two tangent theorems:
- Alternate segment theorem
As you can see, there are actually two tangent theorems, but in GCSE Maths we count these as two parts of the same theorem.
There is another useful fact about circles, although this is not usually classed as a circle theorem:
You might see some websites that say there are eight or nine circle theorems. That will usually be because they are counting both tangent theorems, and/or the two radii rule.
See also
- Parts of a circle
- Perpendicular bisector of chord theorem
- Angle at the centre of a circle is twice the angle at the circumference
- Angle in a semicircle is 90°
- Angles in the same segment of a circle are equal
- Opposite angles in a cyclic quadrilateral add up to 180°
- Tangent and radius of a circle meet at 90°
- Two tangents from a point have equal length
- Alternate segment theorem
- Two radii form an isosceles triangle
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