GEOMETRIC CONSTRUCTION: TANGENTS OF A CIRCLE

Tangent and Normal to a Circle

A tangent is a straight line that touches the circumference of a circle. It is usually at right angles to the radius of the circle.

A normal is a straight line which joins the center of a circle to the tangent at the point of tangency.

Evaluation     

Draw a circle indicating its tangent and normal to the tangent

Construction of Tangent and Normal to a circle

Tangent to a circle from a point on the circumference

Steps

1. Draw the circle with center O
2. Mark the given point A on the circumference
3. Join OA and extends it outwards
4. With A as center and radius OA, draw an arc to cut the extended line at B
5. The perpendicular bisector of OB is the required tangent
6. CD is the tangent to the circle at point A while OB is the normal

Tangent to a circle from a given point outside the circle

Steps

1. Draw the given circle with center O
2. Locate point A outside the circle
3. Draw line OA
4. Construct a semicircle on OA to intersect the given circle at B
5. Line AB is the required tangent to the circle

Tangent to a circle from a given point outside the circle

Tangent to two Equal Circles

Steps

1. Draw the two circles with centers A and B respectively
2. Draw line AB to join the two centers
3. Draw a line perpendicular to AB at A to intersect the first circle at D
4. Draw a line perpendicular to AB at B to intersect the second circle at C
5. CD is the required tangent

EVALUATION

1. Construct a tangent to a circle of radius 4cm at any point on the circumference.