# Lesson Notes By Weeks and Term - Junior Secondary School 2

CONSTRUCTION OF TANGENT TO A CIRCLE

FIRST TERM

SUBJECT: BASIC TECHNOLOGY

CLASS: JSS 2

REFERENCE MATERIALS

1. MELROSE, Basic Science and Technology, Book 2
2. NERDC, Basic Technology for JSS, Book 2

WEEK TEN

TOPIC: CONSTRUCTION OF TANGENT TO A CIRCLE

CONTENT

• Construction Of Tangent To A Given Circle.

HOW TO CONSTRUCT A TANGENT TO A CIRCLE AT A GIVEN POINT ON THE CIRCUMFERENCE

Procedure

1. Draw the given circle with centre O
2. Indicate the given point P.
3. Draw a line from centre O to pass through point P to extend outside the circle.
4. With centre P and radius OP, draw an arc to cut the extended line at A.
5. Bisect line OA.
6. Join the bisecting points with a line BC
7. BC is the required tangent

HOW TO CONSTRUCT A TANGENT TO A CIRCLE FROM A GIVEN POINT OUTSIDE THE CIRCLE

Procedure

1. Draw the given circle with centre O.
2. Indicate the point P to centre O
3. Join point P to the centre O.
4. Construct a semicircle on OP to cut the circle at A.
5. A is point of tangency on the circle.
6. Draw a line to join P to A to give the required.

HOW TO CONSTRUCT A CIRCLE OF A GIVEN RADIUS TO TOUCH A GIVEN STRAIGHT LINE AND CIRCLE

Procedure

1. Draw the given straight line AB, and a circle O
2. Draw a line parallel to line AB at a distance equal to the radius of the required circle.
3. Take this length (radius of required circle R2 + radius of given circle R1.
4. With O as centre, draw an arc to cut the parallel line at C.
5. With centre C and radius CD, draw required circles.

HOW TO CONSTRUCT A CIRCLE TO TOUCH THREE GIVEN LINES

Procedures

1.  Draw the three given lines.
2. Bisect the two angles.
3. The Bisecting lines should be extended to intersect at O.
4. O is the centre of the required circle.
5. Draw a line perpendicular to any side from centre O to give A.
6. With centre O and radius OA draw the required circle.

HOW TO CONSTRUCT A CIRCLE OR AN ARC OF A GIVEN RADIUS TO TOUCH TWO GIVEN CONVERGING LINES

Procedure

• Draw the given lines AB and AC
• Draw lines parallel to AB and AC at a distance equal to the radius R of the circle.
• Extend the lines to intersect at O.
• Draw a line perpendicular to AB or AC from O.
• With centre O, and radius OD draw the arc to touch the two converging lines.

EVALUATION

1. Draw a tangent to a circle of radius 40mm from a point ‘P ‘80mm outside the circle.
2. With the aid of compasses and a ruler construct angle 600 and 300

Read more on construction of tangents.

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

WEEKEND ASSIGNMENT

1. The angle that FC makes when constructed perpendicular with line AB is _______ (a) 1800 (b) 2700 (c) 900 (d) 1200
2. The line FC is called __________ (a) vertical (b) perpendicular (c) Horizontal (d) incline
3. Which of the following drawing materials cannot be used to construct a straight line? (a) Compass (b) protractor (c) Ruler (d) pencils
4. Angles that sum up to 1800 is called __________ (a) supplementary (b) complementary (c) Reflex (d) obtuse
5. The line for all visible outlines is called ____________ (a) Thin continuous line (b) Thick continuous line (c) short dashes (d) Zig – Zag lines.

THEORY

1. Draw a tangent to a circle of radius 30mm from a point ‘P ‘70mm outside the circle.
2. With the aid of compasses and a ruler construct angle 600 and 300.