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Circle Geometry
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New Zealand
Level 6 - NCEA Level 1

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.

  1. 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.

  1. 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

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