AQA · Mathematics · 8300
GCSE Maths: Circle theorems – theorems
Geometry & Measures · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths practice questions for Circle theorems – theorems (Corbettmaths Video 64), and every card links back to the exact page it came from. Practice tests generate fresh variations of these questions, so the numbers change every attempt. Source material © Corbettmaths — used with attribution.
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What is the relationship between an angle at the centre and an angle at the circumference subtended by the same arc?
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The angle at the centre is twice the angle at the circumference.
What is the size of any angle in a semicircle (angle subtended by a diameter at the circumference)?
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90 degrees. Any angle in a semicircle is a right angle.
What is the sum of opposite angles in a cyclic quadrilateral?
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180 degrees. Opposite angles in a cyclic quadrilateral are supplementary.
What is the relationship between a tangent and a radius at the point of contact?
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They are perpendicular (meet at 90 degrees).
What can be said about two tangents drawn to a circle from the same external point?
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They are equal in length.
What is the relationship between angles in the same segment of a circle?
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Angles in the same segment are equal.
What is the relationship between the angle formed by a chord and a tangent, and the angle in the alternate segment?
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The angle between a tangent and a chord is equal to the angle in the alternate segment.
In an isosceles triangle formed by two radii and a chord, what can be said about the base angles?
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The base angles are equal (because the two radii are equal in length).
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