Geometry

UK Secondary (7-11)

Names in 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.

Which of the following is a secant of the attached circle?

GH

AJK

BAB

COI

DCD

EEF

FGH

AJK

BAB

COI

DCD

EEF

F

Which of the shaded areas represent a segment of a circle? Choose all correct options.

$A$

`A`A$B$

`B`B$C$

`C`C$D$

`D`D$A$

`A`A$B$

`B`B$C$

`C`C$D$

`D`D