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# GCSE Maths | Circle Theorems
- URL: https://www.a-level-maths-tutor.com/gcse-maths-circle-theorems/
- Published: 2026-10-07T18:23:36.000Z
- Updated: 2026-10-07T18:23:36.000Z
- Author: Jaisul Naik
- Tags: GCSE Maths

1. **The angle between a tangent and radius is always 90o**
2. **The angle at the centre is always double the angle at the circumference**
3. **The angle formed by a semi circle is always 900.**
4. **Opposite angles in a cyclic quadrilateral add up to 180o.**
5. **Two angles from the same points are equal.**
6. **Angles in the alternate segment are equal.**

### Question 1

![](https://storage.ghost.io/c/ed/77/ed776ea5-c32f-46bf-aa49-8f19b6cd7ac4/content/images/2025/05/Screenshot-2025-05-28-at-13.48.44.png)

Show Question 1 Answers 

a) $x = 25^\\circ$

b) $x = 56^\\circ$

c) $x = 18^\\circ$

### Question 2

![](https://storage.ghost.io/c/ed/77/ed776ea5-c32f-46bf-aa49-8f19b6cd7ac4/content/images/2025/05/Screenshot-2025-05-28-at-13.49.09.png)

Show Question 2 Answers 

a) $x = 102^\\circ$

b) $x = 61^\\circ$

c) $x = 70^\\circ$

### Question 3

![](https://storage.ghost.io/c/ed/77/ed776ea5-c32f-46bf-aa49-8f19b6cd7ac4/content/images/2025/05/Screenshot-2025-05-28-at-13.49.41.png)

Show Question 3 Answers 

a) $x = 50^\\circ$

b) $x = 24^\\circ$

c) $a = 37^\\circ$, $b = 37^\\circ$

### Question 4

![](https://storage.ghost.io/c/ed/77/ed776ea5-c32f-46bf-aa49-8f19b6cd7ac4/content/images/2025/05/Screenshot-2025-05-28-at-13.49.54.png)

Show Question 4 Answers 

a) $x = 83^\\circ$, $y = 104^\\circ$

b) $x = 130^\\circ$, $y = 95^\\circ$

c) $x = 109^\\circ$, $y = 140^\\circ$

### Question 5

![](https://storage.ghost.io/c/ed/77/ed776ea5-c32f-46bf-aa49-8f19b6cd7ac4/content/images/2025/05/Screenshot-2025-05-28-at-13.50.19.png)

Show Question 5 Answers 

a) $x = 63^\\circ$

b) $x = 22^\\circ$

### Question 6

![](https://storage.ghost.io/c/ed/77/ed776ea5-c32f-46bf-aa49-8f19b6cd7ac4/content/images/2025/05/Screenshot-2025-05-28-at-13.50.37.png)

Show Question 6 Answers 

a) $x = 70^\\circ$

b) $x = 55^\\circ$, $y = 60^\\circ$

c) $x = 65^\\circ$, $y = 63^\\circ$, $z = 52^\\circ$

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