Circle

A circle is a plane figure bounded by a curved line called the circumference. All the points on the circumference of a circle are equidistant from a point called the centre.

PARTS OF A CIRCLE

• Diameter

The diameter is a straight line drawn through the centre of a circle and meeting the circumference at both ends.

• Radius 

The radius is a straight line drawn from the centre of a circle to any point on the circumference of the circle. The length of the radius is always used to draw the circle.

• Segment

The segment is an area of the circle bounded by an arc and a straight line called the chord.    

• Chord

The chord is a straight line which joins any two given points on the circumference of a circle.

• Sector

The sector is part of the circle bounded by two radii and an arc.

• Quadrant

The quadrant is the part of the circle bounded by two radii which are at right angles to each other, bounded by an arc. The quadrant, as the name, is ¼ of the circle.

• Tangent

The tangent is usually formed outside the circle. When a straight line touched is formed. However, that line must be right angle to a radius

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EVALUATION

1. Draw a circle 30mm and show the different parts.
   1. Explain each part of a circle

HOW TO DRAW A CIRCLE GIVEN THE RADIUS

Procedure

1. Draw the centre lines horizontally, and the other vertically, to intersect each other at E at 90⁰.
2. The point of intersection is the centre. With the compass at centre E, pick the given radius into the compasses.
3. The point of intersection E, is the centre of the circle. Place the pinpoint of the compasses on the centre and swing the pencil round such that the pencil makes 360⁰ to give the circle.

HOW TO CONSTRUCT A CIRCLE THROUGH A THREE POINTS WHICH ARE NOT ON A STRAIGHT LINE

Procedure

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

HOW TO DRAW A SERIES OF CIRCLES TOUCHING ONE ANOTHER ON THE TWO CONVERGING LINES

Procedure

1. Copy the given converging lines AB and AC.
2. Bisect the angle between the converging lines BA and CA.
3. Draw a line from A to pass through D.
4. AE is the bisector, and the centre of the circles is located on the bisector.
5. Draw the largest circle by placing the point of the compasses somewhere on the bisector and adjust the pencil point, until the required radius is obtained.
6. Draw a tangent FG to the circle at point of intersection between the circumference of the circle and the bisector .
7. Bisect the angle IJA
8. Draw a line through point K to intersect main bisector AE at L.
9. Note that point L is the centre for smaller circle.
10. With centre L draw the smaller circle to touch the bigger circle tangentially.

HOW TO FIND CENTRE OF A CIRCLE  

Procedure

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

EVALUATION

1. Draw a circle of diameter 80 mm and determine its centre.
   1. Draw three circles of diameter 40mm touching each other

READING ASSIGNMENT

Read construction of tangents to a circle

1. MELROSE, Basic Science and Technology, book 2 page 73-76
   1. NERDC, Basic technology for JSS book 2, page 44-45.

WEEKEND ASSIGNMENT

1. The part of the circle that is bounded by an arc or cord is (a) segment (b) sector (c) diameter (d) tangent.
2. A straight line drawn through the centre, meeting the circumference at both ends is called (a) sector (b)radius (c) diameter (d) tangent
3. A plane figure bounded by a curved line called circumference is called——-(a) triangle (b) circle (c) quadrilaterals (d) curved line
4. Any straight line drawn across the circle, meeting the circumference at both ends is called (a) chord (b) tangent (c) radius (d) diameter
5. Which of the following can be used to draw a circle? (a) protractor (b) French curve (c) compass (d) template

THEORY

1. Draw a circle of radius 35mm and divide it into 12 equal sizes.
2. Draw a circle and with shaded portion show (i) quadrant (ii) sector (iii) segment inside the circle.