Circle Theorem Cyclic Quadrilateral

IGCSE Circle Theorems Revision

Year 11 Miss Hancock

​Before we start to revise circle theorems, let's review what we know about angles.

​

​Please write down anything in this picture you were not confident on!

​

​You can come back to this slide as well.

Multiple Choice

What is the sum of the degrees of the interior angles of a 19-gon?

• 3420 degrees

• 3060 degrees

• 3780 degrees

• 3530 degrees

Fill in the Blanks

What is the size of angle x? 

You must give a reason on the next question!

Multiple Choice

The reason for my answer is...

• It is vertically opposite

• It is co-interior

• It is parallel

• It is alternate

Multiple Choice

If the sum of the interior angles of a polygon is 1800°, how many sides does it have?

*Hint* - Use your equation, but plug your value for S in and now solve for n.

• 10 sides/ Decagon

• 12 sides/ 12-gon

• 8 sides/ Octagon

• 11 sides/ 11-gon

Exterior Angles

Remember : the sum of the exterior angles for any polygons is always 360 degrees!

Fill in the Blanks

What is the measure of each exterior angle of a regular decagon (10 sides) ?

*Hint* Regular means all of the sides and all of the angles are equal, including the exterior angles.

Multiple Choice

Select the correct values for a and m.

• a=50, m=89

• a=50, m=116

• a=105, m=89

• a=105, m=116

Fill in the Blanks

Solution

Add up all the angles:

90 + 60 + 46 + 73 = 269

Subtract from 360:

360 - 269 = 91

answer:

x = 91

Multiple Choice

Solve for x.

• 5

• 12

• -7

• -6

Multiple Choice

Solve for x.

• 16

• 11

• 50

• 6

Multiple Choice

• 36

• 108

• 27

• 45

​CHECKPOINT!

​If at this point you would like to do some more practice on these type of questions (Angles in Parallel lines, polygons and exterior/interior angles)

​That is absolutely fine!

​

Please head now to Dr Frost where there are questions and videos to help you.

Circle Theorems

Circle Theorem

The angle in a semi-circle is a right angle.

Circle Theorem

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

Circle Theorem

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

Circle Theorem

Angles in the same segment are equal

Circle Theorem

Circle Theorem

The perpendicular from the centre to a chord bisects the chord.

Circle Theorem

Two tangents from a point to a circle are equal.

Circle Theorem

The tangent to a circle is perpendicular to the radius at the point of contact.

Time for some questions

Let's see what you've learned...

Multiple Choice

What is the measure of angle c and d?

• c = 21, d = 50

• c = 63, d = 78

• c = 78, d = 63

• c = 10, d = 50

Multiple Choice

what are the values of c and d?

• c = 218, d = 71

• d = 109, c = 71

• c = 142, d = 218

• c = 142, d = 109

Multiple Choice

Find the value of the angle marked x....

• 90

• 43

• 47

• 53

Multiple Choice

Find the value of the angle marked x....

• 50

• 100

• 80

• 90

Multiple Choice

I am called a...

• Chord

• Tangent

• Arc

• Line

​Now to practice some exam questions...

​See link on classroom

​

​https://corbettmaths.com/wp-content/uploads/2013/02/circle-theorems.pdf