UK Secondary (7-11)
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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.

 

Worked Examples

Question 1

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

  1. GH

    A

    JK

    B

    AB

    C

    OI

    D

    CD

    E

    EF

    F

    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.

  1. $A$A

    A

    $B$B

    B

    $C$C

    C

    $D$D

    D

    $A$A

    A

    $B$B

    B

    $C$C

    C

    $D$D

    D

 

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