CONSTRUCTION OF TANGENT TO A 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 R_1.
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

READING ASSIGNMENT

Read more on construction of tangents.

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

WEEKEND ASSIGNMENT

THEORY

Draw a tangent to a circle of radius 30mm from a point ‘P ‘70mm outside the circle.

1. With the aid of compasses and a ruler construct angle 60⁰ and 30⁰.