Circle – JSS2 Basic Technology Lesson Note (First Term)

A circle is a plane figure bounded by a curved line called the circumference, with every point on that line the same distance from a fixed point called the centre.

Behavioural objectives

1. Define a circle.
2. Name and describe the parts of a circle.
3. Draw a circle when the radius is given.
4. Construct a circle through three points that are not in a straight line.
5. Find the centre of a given circle.
6. Draw a series of circles touching one another between two converging lines.

What is a circle?

A circle is a closed plane figure whose boundary is at the same distance from the centre at every point.

• Plane figure: a flat shape that can be drawn on paper.
• Circumference: the curved line that bounds the circle. It is also the distance round the circle.
• Centre: the fixed point inside the circle. All points on the circumference are equidistant from it.
• Examples: a coin, a bicycle wheel, a plate and the top of a drum.

What tools are used to draw a circle?

A circle is drawn with a pair of compasses and a pencil, together with a ruler and a set square for the lines.

• Compasses: one leg has a pinpoint for the centre and the other holds the pencil.
• Pencil: a sharp HB pencil gives a clear, thin line.
• Ruler: sets the radius on the compasses and draws straight lines.
• Set square: draws lines at 90°, such as the centre lines.

What are the parts of a circle?

There are seven main parts of a circle: diameter, radius, segment, chord, sector, quadrant and tangent.

• Diameter: a straight line drawn through the centre of a circle and meeting the circumference at both ends.
• Radius: a straight line drawn from the centre of a circle to any point on the circumference. Its length is always used to draw the circle.
• Segment: an area of the circle bounded by an arc and a straight line called the chord.
• Chord: a straight line that joins any two given points on the circumference of a circle.
• Sector: part of the circle bounded by two radii and an arc.
• Quadrant: part of the circle bounded by two radii at right angles to each other, and by an arc. A quadrant is ¼ of the circle.
• Tangent: a straight line that touches the circle at one point only. It lies outside the circle and is at right angles to the radius drawn to the point of contact.

What other terms are used with circles?

• Arc: any part of the circumference.
• Semicircle: half of a circle, cut off by a diameter.
• Centre lines: a horizontal and a vertical line crossing at the centre of the circle.

What is the relationship between the radius and the diameter?

The diameter of a circle is twice its radius, and the radius is half the diameter.

• Diameter: d = 2 × r.
• Radius: r = d ÷ 2.
• Example 1: a circle of radius 30 mm has a diameter of 60 mm.
• Example 2: a circle of diameter 80 mm has a radius of 40 mm.

What is the difference between a diameter and a chord?

A diameter is a straight line through the centre that meets the circumference at both ends. A chord is a straight line joining any two points on the circumference.

• Diameter: it is the longest chord of a circle.
• Chord: it may or may not pass through the centre.

How do you draw a circle given the radius?

To draw a circle, set the compasses to the radius and swing the pencil round the centre.

1. Draw two centre lines, one horizontal and the other vertical, to intersect each other at E at 90°.
2. The point of intersection E is the centre of the circle. Set the compasses to the given radius.
3. Place the pinpoint of the compasses on the centre E and swing the pencil round through 360° to give the circle.

How do you construct a circle through three points that are not in a straight line?

Draw the perpendicular bisectors of two lines joining the points, and use their meeting point as the centre.

1. Join the given points A, B and C with straight lines AB and BC.
2. Draw the perpendicular bisectors of AB and BC so that they intersect at point D.
3. The point of intersection D is the centre of the circle. With D as the centre, set the pencil point of the compasses to any of the three given points A, B or C.
4. Swing the compasses through the three points to produce the circle.

How do you find the centre of a circle?

The centre of a circle is found where the perpendicular bisectors of two chords meet.

1. Draw the given circle.
2. Draw any two chords AB and AC.
3. Draw the perpendicular bisectors of AB and AC. The bisectors will intersect at O.
4. O is the centre of the circle.

How do you draw a series of circles touching one another between two converging lines?

The centres of all the circles lie on the bisector of the angle between the converging lines.

1. Copy the given converging lines AB and AC.
2. Bisect the angle BAC and draw the bisector from A. Call it AE.
3. The centres of all the circles will be located on the bisector AE.
4. Draw the largest circle by placing the point of the compasses on the bisector and adjusting the pencil point until the required radius is obtained.
5. Draw a tangent FG to the circle at the point where the circumference meets the bisector, on the side nearer A.
6. Let the tangent cut the converging lines at I and J. Bisect the angle AJI.
7. Extend this bisector to cut the main bisector AE at L.
8. Point L is the centre of the next smaller circle.
9. With centre L, draw the smaller circle to touch the bigger circle tangentially.
10. Repeat steps 5 to 9 on the smaller circle to draw more circles.

What mistakes should you avoid when drawing circles?

• Loose compasses: tighten the hinge so the radius does not change while drawing.
• Blunt pencil: a thick line makes the circle inaccurate.
• Wrong radius: do not use the diameter as the radius.
• Faint bisectors: keep construction lines light but clear so the centre can be seen.
• Slipping pinpoint: hold the pinpoint firmly at the centre while swinging the pencil.

Evaluation

1. Draw a circle of radius 30 mm and show the different parts.
2. Explain each part of a circle.
3. Draw a circle of diameter 80 mm and determine its centre.
4. Draw three circles of diameter 40 mm touching each other.

Assignment

1. Define a circle and list its seven parts.
2. Mark three points A, B and C that are not in a straight line, then construct a circle through them.