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.
Worked Examples
Question 1
Which of the following is a secant of the attached circle?
GH
A
JK
B
AB
C
OI
D
CD
E
EF
F
Question 2
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
Outcomes
10.G.C.1
Tangents to a circle motivated by chords drawn from points coming closer and closer to the point. (a) The tangent at any point of a circle is perpendicular to the radius through the point of contact. (b) The lengths of tangents drawn from an external point to a circle are equal.