Difference between revisions of "Geogebra/C3/Tangents-to-a-circle/English"

Welcome to this tutorial on "Tangents to a circle in Geogebra".

Slide Number 2 Learning Objectives

At the end of this tutorial you will be able to

• Draw tangents to a circle
• Understand the properties of Tangents

Pre-requisites

If not,

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System Requirement

Ubuntu Linux OS Version 11.10

Geogebra Version 3.2.47.0

GeoGebra Tools used

• Tangents
• Perpendicular Bisector
• Intersect two Objects
• Compass
• Polygon
• Circle with Center and Radius

Dash home >>Media Apps>>Under Type >>Education>>Geogebra

Click on Dash home Media Apps. Under Type Choose Education and GeoGebra.

let's define tangents to a circle

Definition of a tangent

Show the finished figure

The point of contact is called "point of tangency"

Graphic view box opens>> un-check on Axes>>Select Grid

Right Click on the drawing pad

In the "Graphic view"

uncheck "Axes"

Select "Grid"

Select “Circle with Center and Radius” tool

Mark a point 'A' on the drawing pad

Click OK

Visually show that you can move point 'A', but the circle remains of the same radius.

Click OK

A circle with centre 'A' and radius '3' cm is drawn.

Let's 'Move' the point 'A' and see that circle has same radius

Mark a point 'B' outside the circle

Join points 'A' and 'B'. Segment AB is drawn

Move the point B and show how the perpendicular bisector moves along with B.

Mark points 'A' and then 'B'

A perpendicular bisector is drawn

Let's Move the point 'B' and see how the 'perpendicular bisector' moves along with 'B'.

Again, move point 'B', and show that 'C' moves accordingly.

Click on "Intersect two objects" tool

Mark point of intersection as 'C'

Let's Move point 'B', and see how point 'C' moves along with 'B'

Click on "Distance" tool. click on points 'A' , 'C'. and 'C' ,'B'

Notice that 'AC' = 'CB'

Click on points 'C', 'B'. and 'C' once again... to complete the figure.

Point to the two points of intersection

Click on "Intersect two objects" tool Mark the points of intersection as 'D' and 'E'

Join points 'B' and 'D'. 'B' and 'E' .

join points 'A', 'D' and 'A', 'E' Segment 'AD'=Segment 'AE' (radii of circle 'c').

Point to Segments 'AD' and 'AE'

Segment 'AD'= segment 'AE'

Let's check from Algebra view

Outine the semicircle 'd'.

Lets check with "Angle" tool

Click on the points 'A', 'D', 'B' and 'B', 'E', 'A'

Outline the two triangles

therefore '△ABD' '≅' '△ABE' by "SAS rule of conguency"

we can find that the tangents 'BD' and 'BE' are equal

A tangent is always at right angles to the radius of the circle where it touches

Click on “File”>> "Save As"

I will type the file name as "Tangent-circle" Click on "Save"

Click on “File”>> "Save As"

I will type the file name as "Tangent-circle" Click on "Save"

Theorem

click on “File” >> "New"

Click on point 'A' as center, then on point 'B'.

Mark points 'C' on circumference of the circle and point 'D' outside the circle.

click on point 'D'... and circumference.

Two Tangents are drawn to the circle.

Click on "Intersect two objects" tool>>Mark points of intersection

Click on "Intersect two objects" tool Mark points of intersection as 'E' and 'F'.

Click on the "Polygon" tool.

Click on the points 'B' 'C' 'F' and 'B' once again to complete the figure

Click on "Angle" tool click on the points 'F' 'C' 'B' and 'D' 'F' 'B'

I will type the file name as "Tangent-angle" Click on "Save"

Click on “File”>> "Save As"

I will type the file name as "Tangent-angle" Click on "Save"

With this we come to the end of this tutorial.

In this tutorial, we have learnt to verify that

"Two tangents drawn from an external point are equal"

"Angle between a tangent and radius of a circle is 90^0"

"Angle between tangent and a chord is equal to inscribed angle subtended by the chord "

"Angle between tangents drawn from an external point to a circle, is supplementary to the angle subtended by the line-segment joining the points of contact at the centre".

To verify the theorem

Draw a circle

Draw tangents from an external point

Mark points of intersection of the tangents

Join center of circle to intersection points

Measure angle at the center, and

Measure angle between the tangents

What is the sum of the two angles?

Join center and external point

Does the line-segment bisect angle at the center?

Hint - Use Angle Bisector tool

Sum of the angles =180^0. The line bisects the angle

Acknowledgement

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Script – contributed by Neeta Sawant from SNDT Mumbai

Naration- Madhuri Ganpathi from IIT Mumbai

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