Construction of Tangent and Normal to a Circle

Construct a Tangent to a Circle at a given Point to the Circle:

S/N	Steps	Activity
1.	Indicate a point P somewhere on a given circle, with centre point O.
2.	Draw a straight line from the centre O, through the given point P outward.
3.	With the compass on centre P and a width less than distance OP, draw an arc on each side of P. This creates the points Q and R as shown.
4.	Set the compass on Q and set it to any width greater than the distance QP.
5.	Without changing the compasses’ width, draw an arc approximately in the position shown on one side of P.
6.	Without changing the compasses’ width, move the compasses to R and make another arc across the first, creating point S.
7.	Draw a line through P and S.
8.	Done. The line PS just drawn is the tangent to the circle O through point P.

Construct a Tangent to a Circle from a Point Outside a Circle:

Steps:

1. Draw a circle with centre O.

2. Indicate the given point P outside the circle.

3. Draw line OP.

4. Bisect the Line OP

5. Construct a semi-circle to cut the circle at A.

6. Draw a line from P through A. The line is the tangent.

Construct Tangent to Two Equal Circles:

1. Draw two circles as shown below;

2. Draw a line through the centre of the circles, and label the diameters of each circle as shown below.

3. Bisect the diameters AB and CD. The bisectors cut the circumference of the circles at E and F.

4. Draw a line through E and F. This line is the tangent.