
1. Open GeoGebra. We will need the Algebra window
and the Axes so be sure that they are displayed.
If not, use the View menu from the menu bar to
show them.


2. We will only need to label of the points, so we will not
GeoGebra automatically label other objects. To do this,
click the Options menu, click Labeling,
then click All New Points Only.


3. To create a slider r for the radius of our
circle, select the Slider tool, then click
anywhere on the drawing pad to display the Slider
dialog box.


4. In the Slider dialog box, type r in
the Name box, type 0.1 in the min
box, and leave the max value as 5 and increment as
0.1, then click the Apply button.
Figure 1 – The Slider dialog box.


5. Create another slider name it
n, set the minimum to 3,
maximum to 30 and increment to 1. Slider
n, will determine the number of sides of our
inscribed polygon.


6. Next, we do not want any new objects to have labels. To
do this, click the Options menu, click
Labeling then click No New
Objects.


7. To construct a circle with center A and radius r, type
circle[A,r] .
Move slider r and see what happens.


8. To construct the intersection of the circle and the
xaxis, type (r,0) in the input box and
press the ENTER key.


9. Now, we compute for the central angle of our inscribed
polygon. To do this, we divide 360 by n. For
example, if we want to have an equilateral triangle, we
must divide 360 by 3, which will be our central angle. To
do this, type a =
(360/n)° then press the ENTER key. The degree sign,
tells GeoGebra that a is an angle measure. You can display
the degree sign by selecting it at the drop down list box
right next to the input box.


10. To create angle BAB’, click the Angle
with Given Size tool, click point B and
click point A. This will display the Angle
with Given Size dialog box.


11. In the Angle dialog box, type a in the
Angle text box and choose the counter clockwise
button and then click the OK button. Your
drawing should look like the one shown in Figure 2.
Figure 2  Central angle BAB'.


12. To hide the angle measure (green sector), right click
it then click Show Object.


13. To construct the inscribed polygon, select the
Regular Polygon tool, click B and
then click B’. This will display the Regular
Polygon dialog box.


14. In the Regular Polygon dialog box, type
n.
This means, that we want to inscribe a polygon with n
sides, then click the Ok button.. Now, drag slider
n and see what happens. If you set n to
30, your drawing should look like the one shown in Figure
3.
Figure 3  A circle with an inscribed 30sided polygon.


15. Our problem now is to hide the labels of all the points
and the segments. With n set to 30, right click
the polygon, then click Properties from the
context menu.


16. In the Properties dialog box, select the
Basic tab, click Point (be sure that the
Point text is highlighted) in the Objects list,
and uncheck the Show Label check box. This will
hide the labels of all the points. Now, click Segment text
and uncheck the Show Label check box to hide the
labels of all the sides of the polygons.
Figure 4  The Properties dialog box.


17. Now, using the text tool, we will display the area of
the circle and the area of the inscribed triangle. To
display the area of the circle, click the Insert
Text tool and click anywhere and type the
following:
“The area of the
circle with radius ” + r + “is ” + pi*r^2.
The blue text enclosed by double quotes are constants and
will exactly appear as they are. The red texts r
and pi*r^2 are variables and will display
numbers based on the value of the slider r and
the result of the computation. GeoGebra interprets pi as
the mathematical constant which approximately equals
3.1416. Note that constants are always enclosed by double
quotes. Constants and variables are always separated by
the + symbol.


18. Use the text tool to display the entire polygon. In the
Text tool, type
“The area of the
inscribed polygon is “ + poly1
Note that poly1 is the area of our polygon (see the
Algebra window). Adjust the positions of the text as
needed. Move the sliders and observe what happens.


19. Your drawing should look like the Figure below. (The
font of the text has been resized to make it more visible
in the drawing).
Figure 5  Final output.


20. What is the relationship between the area of the circle
and the and the area of the inscribed polygon?
