NZ Level 6 (NZC) Level 1 (NCEA) Parts of Circles
Lesson

We've already looked at a couple of different features of a circle including the:

• circumference: the distance around the edge of the circle.
• diameter: the distance from one side of the circle to the other, passing through the centre.
• radius: the distance from the centre of the circle to the edge.

Now we a going to look at a couple of new parts of a circle. Let's start by checking out the picture below. Now let's explain each of these features.

• Tangent: a line that intersects the circumference of a circle in exactly one point. A tangent is perpendicular to the radius from the point where the tangent touches the circle.
• Arc: part of the circumference of the circle.
• Chord: a line that goes from one point to another on the circle's circumference, without passing through the centre.
• Sector: a section of the circle defined by two lines from the centre to the circumference. It looks like a piece of pizza. However, there are different kinds of "slices." A minor sector has an angle at the centre of the circle of less than $180^\circ$180°. A major sector has an angle at the centre of the circle of more than $180^\circ$180°. There are are some special kinds of sectors:
• Semicircle: a sector made from half the area of a circle.
• Quadrant: a sector made from a quarter of the area of a circle.
• Segment: an area made from a chord and an arc of the circle. Each chord produces two segments: a major segment (the large shape) and the minor segment (the small shape, like the one shaded in the picture above).
• Secant: a line that touches and passes through two points on a circle's circumference.
• Cyclic quadrilateral: a four-sided shape whose four points touch the circumference of a circle.

Now we've gone through all these different parts of a circle, you can play around with this applet to make sure they're all clear.

#### Worked Examples

##### Question 1

Which of the following is a tangent of the attached circle? 1. CD.

A

AB.

B

GH

C

OF.

D

EO

E

JK.

F

CD.

A

AB.

B

GH

C

OF.

D

EO

E

JK.

F

##### Question 2

Which of these areas is a minor sector? 1. 3

A

1

B

2

C

4

D

3

A

1

B

2

C

4

D

### Outcomes

#### GM6-4

Deduce and apply the angle properties related to circles

#### 91031

Apply geometric reasoning in solving problems