ASSIGNMENT 7

BY

SHADRECK S CHITSONGA

TANGENT CIRCLES

This write up is about tangent circles. But before we do that let us first of all look at something that most of us are familiar with, tangent and a circle, since we have always associated a line as being a tangent to a circle.

A simple definition of a tangent says that a tangent to a circle is a line that touches a circle at one point only. Unlike the secant the tangent does not cut through the circle.

1. A tangent on a circle. The thick blue line is the tangent to the circle. The point B is called

the point of contact. There is an important theorem about this tangent and the circle

Theorem: Radius is perpendicular to the circle at the point of contact

2. Tangent to a circle from an external point

THEOREM

The tangents to a circle from an external point are equal and make equal angles

with the line joining that point to the centre.

CLICK here to move point A to see how AB and AC change. AB and AC are the two tangents

to the circle. There can only be two tangents to a circle from a given fixed point.

3. An interior tangent common to two unequal circles.

Do you know why AB = CD?

NOTE: The construction marks are left out just to demonstrate the steps involved in the

construction.

4. An exterior tangent common to two unequal circles

There are a number of things that one can explore with tangent lines. Most of them have to deal with lines and angles.

TANGENT CIRCLES

1. A circle that touches two circles that do not touch each other.

OB c IB = 5.01 cm

CO c GA = 3.86 cm

2. Another possibility if we do not know the radius of the tangent circle is to do the

construction shown here.

3. A tangent to two unequal circles touching them internally.

The pink circle is the tangent circle.

4. It is also possible for the circles to touch each other externally as shown below.

5. What about if we want three circles to touch each other such that the other two

circles are inside the bigger circle?

END