Parts of Circles

Lesson

Practice

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.

Created with Geogebra

Worked Examples

Question 1

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

A circle with center labeled $O$`O`, is depicted. A line segment $OI$`OI` is drawn from the center to the point $I$`I` on the circumference. Line segment $EF$`EF` passes through the center $O$`O` from point $E$`E` to its opposite point $F$`F`, both points lie on the circumference. Line segment $GH$`GH` is drawn inside the circle, not passing through the center, from point $G$`G` to point $H$`H`, both points lie on the circumference. Points $C$`C` and $D$`D` are points outside the circle, a line segment $CD$`CD` passes through the circle but not passing through the center. $AB$`AB` is a line segment that touches the circle at an unlabeled point. The circle has a thick black arc on the bottom, labeled arc $JK$`JK`.

CD.
A
AB.
B
GH
C
OF.
D
EO
E
JK.
F

Question 2

Which of these areas is a minor sector?

Three circles have some of its area shaded in orange. The first circle has two areas shaded, one labeled as "$1$1" and the other labeled as "$2$2". Area "$1$1" is the area enclosed by the two radii and their intercepted arc. Area "$2$2" is enclosed by a chord and its intercepted arc. The second circle has an area labeled as "$3$3." Area "$3$3" has half of its area shaded which is enclosed by the diameter and its intercepted semicircular arc. The third circle has an area labeled as "$4$4." Area "$4$4" is enclosed by four chords intersecting at four points on the circumference such that it forms an inscribe quadrilateral.

3
A
1
B
2
C
4
D

Outcomes

12CT.D.3.1

Recognize and describe (i.e., using diagrams and words) arcs, tangents, secants, chords, segments, sectors, central angles, and inscribed angles of circles, and some of their real-world applications (e.g., construction of a medicine wheel)