Understanding Engineering Mathematics

5.2.9 Lines and angles in a circle

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Figure 5.20 reminds you of the main definitions relating to a circle.

Centre Centre

Diameter

Radius

Major

sector

Minor

sector

Tangent

Minorarc

Major segment

Minor segment

Majorarc

Figure 5.20Definitions in circles.

There is not much that can be said about the circle in isolation, other than to note its
perfect symmetry and the standard perimeter formula ‘2πr’ and area formula ‘πr^2 ’where
ris the radius. It is when you start considering parts or arcs of the circle, or particular
lines related to the circle that things get interesting. First note that, in geometry, we are
not concerned so much withmeasuringaspects of the circle or its parts. We are more
concerned about relations between them, independent of numerical values. An example
would be the result that chords which are equidistant from the centre are of the same
length. This result does not help in calculating the lengths of chords, it simply states a
relationship between certain types of chords. Two obvious lines of importance are the
radius and tangent. As shown in Figure 5.20 the tangent is perpendicular to the radius at
its point of contact.
Consider anarcof a circle – a connected part of the circumference. If the arc has length
less than half of the circumference then it is called aminor arc, otherwise it is amajor
arc. In Figure 5.21

A

B

O

D

C

Figure 5.21Angles subtended by arcs.