Circle (Parts of a Circle, Dividing a Circle)

A circle can be defined as the locus of points, moving from a fixed point which is the centre of the circle to a fixed distance, which is the circumference.

The circumference is always equidistant from the centre.

Parts of a Circle:

Parts of the circle include:

i. Circumference: This is a curved line around a circle or the outer part of a circle.

ii. Diameter: It is a straight line that passes through the centre of a circle and touches the circumference at both sides.

iii. Radius: It is a straight line drawn from the centre of a circle to touch the circumference.

Radius = \( \frac{diameter}{2} \)

Diameter = Radius × 2

iv. Chord: It is a straight line that joins two points on a circle. which does not necessarily pass through the centre of the circle.

v. Sector: It is the part of a circle lying between two radii and an arc.

vi. Quadrant: This is a quarter of a circle.

vii. Segment: This is a part of a circle separated from the rest by a straight line joining two points on the outer edge.

viii. Tangent: This is a line that intersects the circle exactly in one single point. The point of tangency is the point where the tangent touches the circle. At the point of tangency, a tangent is perpendicular to the radius.

Types of Circles:

i. Concentric Circles: These are circles that have the same centre but different radii. e.g.

ii. Eccentric Circles: These are circles that have different centres and different radii.

Dividing a Circle into Equal Parts Steps:

To divide a circle into (n) equal parts we will be using a set square, T-square and compass.

Note: Use the following centre rule;

\(\frac{360}{n} \)

For example, if the task is to divide into 8 equal parts, n = 8

⇒ \(\frac{360}{8} \\ \scriptsize = 45^o \)

Use 45° set square

If 12 equal parts, n = 12

⇒ \(\frac{360}{12} \\ \scriptsize = 30^{/circ} \)

Use 30° set square

Dividing a Circle into Four Equal Parts:

Steps:

• Use your Tee square and set square to draw equal horizontal diameter AB and vertical diameter CD (e.g. 60 mm) to intersect at O. These lines will be the diameter of the circle, therefore the radius will be half of the diameter (e.g. 30 mm)

• With O as the centre and the given radius, use your compass to draw the given circle. 

• Quadrant 1, 2, 3, and 4, is the required division.

Dividing a Circle into Eight Equal Parts:

Steps:

• Draw a circle with a compass.

• First, divide it into four equal parts as described above.

• Slide the tee square below the horizontal line. Use the 45°/45° set square to draw lines at 45°.

• Repeat the procedure on the other side or quadrant of the circle.

• Join the lines through the centre to the circumference of the circle, see the figure below.

Dividing a Circle into Twelve Equal Parts:

Method 1:

Steps:

• Draw a circle with a compass.

• Divide the circle into 8 equal parts with the 45°/45° set-square.

• Place the 30°/60° set-square and draw a line with the 30° side through the centre of the circle to trace the circumference on both sides

• Repeat this with the 60° side of the set square. See the figure below.

Method 2:

Steps:

• Draw a circle of a given radius with centre O

• Use your Tee square and set square to draw equal horizontal diameter AB and vertical diameter CD (e.g. 60 mm) to intersect at O.

• Using your compass, with centres A, B, C and D in turn and the radius of the given circle, draw arcs 1 and 2.

• Draw diameters from 1 to 2 in opposite directions.

• The circle is now divided into 12 equal parts.