Day 127 – Tangent to a circle

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.

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

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

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

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.

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

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

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?

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

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