A level: Circle Theorems
This flashcard set explains key circle theorems using memorable visual cues such as “arrowhead,” “butterfly,” and “wheel on a flat surface.” Each card links a geometric figure to its corresponding theorem, making it easier to understand and recall important angle and segment properties within and around circles—ideal for GCSE and high school geometry revision.
Arrowhead
The angle subtended at the centre of the circle is double the size of the angle at the circumference from the same points.
Key Terms
Arrowhead
The angle subtended at the centre of the circle is double the size of the angle at the circumference from the same points.
Butterfly
Angles in the same segment of a circle are equal
Wheel on a flat surface
The angle between the tangent and radius is 90 degrees
Diameter triangle
The inscribed angle in a semicircle is 90 degrees
Rectangle
Opposite angles in a cyclic quadrilateral add up to 180 degrees
Triangle in circle on flat surface
Alternate segment theorem
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| Term | Definition |
|---|---|
Arrowhead | The angle subtended at the centre of the circle is double the size of the angle at the circumference from the same points. |
Butterfly | Angles in the same segment of a circle are equal |
Wheel on a flat surface | The angle between the tangent and radius is 90 degrees |
Diameter triangle | The inscribed angle in a semicircle is 90 degrees |
Rectangle | Opposite angles in a cyclic quadrilateral add up to 180 degrees |
Triangle in circle on flat surface | Alternate segment theorem |
Arrow from circumference of circle | Tangents from a point outside the circle are equal in length |
From centre triangle | The perpendicular from the centre to the chord bisects the chord |