Mathematics

sample deck

GCSE Maths: Circle theorems (video)

The circle theorems — angles at the centre and circumference, cyclic quadrilaterals and tangents — from Corbettmaths. Each card deep-links to the video.

1. What is the relationship between the angle at the center and the angle at the circumference subtending the same arc?

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   The angle at the center is double the angle at the circumference.

2. What is the measure of an angle in a semicircle?

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   90°. This is a special case of the angle-at-center theorem: the diameter makes a 180° angle at the center, so the angle at the circumference is half of that.

3. What is true about angles subtended by the same arc in the same segment of a circle?

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   They are equal.

4. What is the sum of opposite angles in a cyclic quadrilateral?

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   180°.

5. What is true about the lengths of two tangents drawn from the same external point to a circle?

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   They are equal.

6. What is the angle between a radius and a tangent at the point of contact?

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   90°. The radius and tangent are perpendicular to each other.

7. What does the alternate segment theorem state about the angle between a tangent and a chord?

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   The angle between the tangent and the chord is equal to the angle in the alternate segment.

8. How does a radius bisect a chord?

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   A radius can be drawn perpendicular to any chord, bisecting it at 90°.

9. A cyclic quadrilateral is one where each vertex lies on the {circumference} of a circle.

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   circumference

practice preview — fresh every time

1. 2 marks · foundation tier

   Solve: -4x + 24 = 4x

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   x = 3

   Collect the x-terms on one side: -8x = -24, so x = 3.

2. 2 marks · foundation tier

   Solve: -x + 3 = -2x + 4

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   x = 1

   Collect the x-terms on one side: x = 1.

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