1. BLOCKBUSTERS – Circle Theorems
Start off by choosing a tile.
If you answer the question correctly you get a tile. The winner is the first to connect their colours vertically, horizontally or diagonally.
However, the group that missed the question risk revealing the right answer to the opponent. This is just to avoid guesses.
15/11/2018
Created By J. Mills-Dadson

2. Created By J. Mills-Dadson
BLOCKBUSTERS
Circle Theorems A I Q E M B J R F N C K S G O D L T H P
15/11/2018
Created By J. Mills-Dadson

3. Created By J. Mills-Dadson
Angle at the circumference is
half the angle at the center
x = ÷ 2
x = 660
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15/11/2018
Created By J. Mills-Dadson

4. Created By J. Mills-Dadson
Here is a circle with center O.
What is the size of angle x?
Sum of angles in triangles equals 1800.
x =
x = 400
Back
NB 900
15/11/2018
Created By J. Mills-Dadson

5. Created By J. Mills-Dadson
Here is a circle with center O.
What is the size of angle x?
Angle P is equal to angle x.
Angle P is half of 1100 because angle at the circumference is half the angle at the center P
Therefore x = ÷ 2
x = 550
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15/11/2018
Created By J. Mills-Dadson

6. Created By J. Mills-Dadson
Here is a circle with center O.
Calculate the size of angle x.
Angles x and 440 substand on the same chord and are in the same segment.
x = 440
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15/11/2018
Created By J. Mills-Dadson

7. Created By J. Mills-Dadson
Here is a circle with center O.
What is the size of angle x?
Opposite angles of Cyclic Quadrilateral add up to 1800.
x = 1800 – 700
x = 1100
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15/11/2018
Created By J. Mills-Dadson

8. Created By J. Mills-Dadson
Here is a circle with center O.
Calculate the size of angle x.
Angles x and 350 substand on the same chord and are in the same segment.
x = 350
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15/11/2018
Created By J. Mills-Dadson

9. Created By J. Mills-Dadson
Here is a circle with center O.
Lines AB and AC are tangents.
Calculate the size of angle x.
Angle x and angle 700 add up to 1800.
x =
x = 1100
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15/11/2018
Created By J. Mills-Dadson

10. Created By J. Mills-Dadson
Here is a circle with center O.
What is the size of angle x?
Angle at the circumference is half the angle at the center (3600 – 2600 =100)
x = ÷ 2
x = 500
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15/11/2018
Created By J. Mills-Dadson

11. Created By J. Mills-Dadson
Here is a circle with centre O.
Lines AB and AC are tangents.
Calculate the length of line OB (x)
Triangle AOB is a right–angled triangle.
Using Pythagoras,
x 2 = 102 – 82
x 2 = 36 Square roots both sides
x = 6cm
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15/11/2018
Created By J. Mills-Dadson

12. Created By J. Mills-Dadson
Here is a circle with center O.
Line AB is tangent.
Calculate the size of angle x?
Angle x and angle 700 are equal – Alternate Segment Theorem.
x = 700
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15/11/2018
Created By J. Mills-Dadson

13. Here is a circle with center O. What is the size of angle x?
A triangle in a semi-circle is right-angled
x = 900
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15/11/2018
Created By J. Mills-Dadson

14. Created By J. Mills-Dadson
Here is a circle with center O.
Calculate the size of angle x.
Angle at the center is double the angle at the circumference
x = 300 X 2
x = 600
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15/11/2018
Created By J. Mills-Dadson

15. Created By J. Mills-Dadson
Here is a circle with center O.
What the size of angle x?
Angle at the circumference is
half the angle at the center
x = ÷ 2
x = 500
Back
15/11/2018
Created By J. Mills-Dadson

16. Created By J. Mills-Dadson
Here is a circle with center O.
What the size of angle x?
Angle at the center is double the angle at the circumference
x = 650 X 2
x = 1300
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15/11/2018
Created By J. Mills-Dadson

17. Created By J. Mills-Dadson
Here is a circle with center O.
Calculate the size of angle y.
Angles y and 300 substand on the same chord and are in the same segment.
x = 300
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Created By J. Mills-Dadson
15/11/2018

18. Created By J. Mills-Dadson
Here is a circle with center O.
What is the size of angle x?
Opposite angles of Cyclic Quadrilateral add up to 1800.
x = 1800 – 1100
x = 700
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15/11/2018
Created By J. Mills-Dadson

19. Created By J. Mills-Dadson
Here is a circle with center O.
Lines AB and AC are tangents.
Calculate the size of angle x?
Angle x and angle O add up to 3600.
Angle O =
Angle O = 1300 .
x =
x = 2300
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15/11/2018
Created By J. Mills-Dadson

20. Created By J. Mills-Dadson
Here is a circle with center O.
What is the size of angle x?
Angle at the center is double the angle at the circumference
x = 510 X 2
x = 1020
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15/11/2018
Created By J. Mills-Dadson

21. Created By J. Mills-Dadson
Here is a circle with center O.
Line AB is tangent.
Calculate the size of angle x.
Sum of angles in triangle equals 1800.
Radius and tangent meet at 900.
NB 900
x = 900 – 600
x = 300
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15/11/2018
Created By J. Mills-Dadson

22. Created By J. Mills-Dadson
Angle at the center is double
the angle at the circumference
x = 600 X 2
x = 1200
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15/11/2018
Created By J. Mills-Dadson