1. Day 127 – Tangent to a circle

2. Introduction
So far, we understand what a tangent is. That it is a line that touches the circle. It also meets the radius at a right angle at the point where it touches the circle. We have also discussed a number of properties of a tangent to a circle. We would like to proceed to see if we can come up with one. In this lesson, we are going to construct a tangent line from a point outside a given circle to the circle.

3. Vocabulary
Tangent
A straight line that touches the circumference of a circle

4. Constructing a tangent from an external point
Constructing a tangent from an external point. Let us consider the circle of center O shown below and choose an external point as T. T O

5. Draw a line connecting the center to T then bisect it
Draw a line connecting the center to T then bisect it. Let the point of bisection be N. T O

6. T O N
With N as the center, and NO as the radius, draw a two arcs to intersect the circle on either sides of OT. Let the points be G and H respectively.

7. Connect H to T and G to T. Thus, we get two tangents passing through T

8. It can be confirmed that OHT and OGT are right angles.

9. homework
Given a point and the circle whose center is identified and you are required to draw a tangent through to the circle through the given point, what is the very first line are you supposed to draw?

10. Answers to homework
A straight line connecting the point to the center of the circle

11. THE END