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Circle Theorems

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A theorem is a statement that can be proved.

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Parts of a Circle

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Without measuring, I know what type of triangle this is:

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A triangle formed by two radii is isosceles:

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Which of these are isosceles triangles:

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An angle in a semicircle is 900

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Decide if the following is an isosceles triangle, a right-angled triangle or neither:

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200

x

Show that x = 700 Give reasons for your answer.

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​

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1100

y

Work out y. Give reasons for your answer:

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​

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A

B

C

F

G

H

400

x

Work out x. Give reasons for your answer:

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​

________________________________________

y

Show that y = 500. Give reasons for your answer:

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​

________________________________________

A

B

C

F

G

H

800

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200

x

Show that x = 700 Give reasons for your answer:

________________________________________

​

________________________________________

1100

y

Work out y. Give a reason for your answer:

________________________________________

​

________________________________________

A

B

C

F

G

H

300

x

Show that x = 600 Give reasons for your answer:

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​

________________________________________

A

B

C

Work out x. Give a reason for your answer:

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​

________________________________________

A

B

C

200

x

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True or False:��A) Angle ADC is a right angle��B) BAD is an isosceles triangle��C) BDC is an isosceles triangle��D) Angle BDC = 450

A

B

C

D

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The angle at the centre is double the angle at the circumference:

https://www.geogebra.org/m/bUnSxp2P

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Opposite angles in a cyclic quadrilateral sum to 1800

Which angles are opposite?

https://www.geogebra.org/m/CffeUy7J

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Which rule?�1)Angle at the centre is double the angle at the circumference.�2) Opposite angles in a cyclic quadrilateral sum to 1800�3) Neither

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300

x

Find the value of x, give a reason for your answer.

​

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​

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Find the value of y, give a reason for your answer.

​

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​

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720

1050

y

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1200

x

Find the value of x, give a reason for your answer.

​

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​

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Find the value of y, give a reason for your answer.

​

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​

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820

1150

y

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Calculate the missing angles of the following:

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Where a radius meets a tangent is 900

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Two tangents from a point are equal.

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300

x

Show that x = 600

Give reasons for your answer.

A

B

C

A

B

C

D

700

Find the size of angle BDC, give reasons for your answer:

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Work out the value of x

Give reasons for your answer.

200

x

A

B

C

A

B

C

D

400

Find the size of angle BDA, give reasons for your answer:

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Using circle theorems.

Prove that ABO is congruent to ACO.

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Angles in the same segment are equal.

https://www.bossmaths.com/g10a/

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Alternate Segment theorem.

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Dr Frost Worksheet:

https://www.drfrostmaths.com/resource.php?rid=139

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Goal Free Problems:

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Circle Theorem Proofs