Circle theorems (OCR GCSE Maths): Flashcards

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Circle theorems
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Relationship between diameter and radius

Diameter is twice the radius (d=2rd = 2r)

How many points does a tangent touch on a circle?

Exactly one point

Angle at centre vs angle at circumference (same arc)

Centre angle = 2×2 \times circumference angle

Angle in a semi-circle

90°90\degree (right angle)

Angles in same segment of circle

Equal to each other

Sum of opposite angles in cyclic quadrilateral

180°180\degree

Angle between tangent and radius at point of contact

90°90\degree (right angle)

Alternate segment theorem: angle between tangent and chord

Equal to angle in alternate segment

Length of two tangents from external point

Equal in length

Definition of chord

Line segment connecting two points on circumference

Definition of arc

Part of the circumference of the circle

Cyclic quadrilateral definition

Quadrilateral with all vertices on circle's circumference

When centre angle is 180°180\degree in Theorem 1

Circumference angle is 90°90\degree (semi-circle)

Definition of segment in circle

Area between a chord and the circumference

Triangle formed by two tangents from external point

Isosceles triangle

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