## Tangents to a Circle

The dynamic worksheet Tangents to a Circle provides two applets that let students learn how to construct the tangents to a circle through a given point. The first applet allows them to go through the construction step-by-step using a navigation bar. The second applet lets them create this construction on their own. To simplify the construction process the second applet includes a customized toolbar that only shows those tools needed for this specific construction.

### Creating this Mathlet

#### First Applet

In order to create the first of the two interactive applets, you need to change the settings of the GeoGebra window. Therefore, open GeoGebra and hide the algebra window by unchecking "Algebra window" in the menu "View". Then, hide the coordinate axes by unchecking "Axes" in the menu "View".

Now, you are ready to prepare the construction of tangents through a point in respect to a circle that will guide your students through the construction steps.

1. Choose the tool "Circle with center through point" and click on the drawing pad twice to create the center A and a second point B that specifies the radius of the circle. Tip: Using the tool "Move" you are able to change the positions of both points later on.
2. Choose the tool "New point" and create a point C outside the circle by clicking on the drawing pad.
3. Choose the tool "Segment between two points" and connect points A and C.
4. Choose the tool "Midpoint or center" and click on the segment AC to get its midpoint D.
5. Choose the tool "Circle with center through point" and create a circle with center D through point C.
6. Choose the tool "Intersect two objects" and click successively on both circles to get the intersection points E and F.
7. Choose the tool "Line through two points" and connect each of the intersection points with point C.
8. Change the properties of the constructed objects to enhance the layout of your construction.
Tip: Right click (Mac OS: ctrl-click) one of the objects and select "Properties".
9. Display the Navigation Bar for Construction Steps

To save space for the second applet on the dynamic worksheet, the interactive applet showing the construction steps needs to be relatively small. Therefore, we need to decrease the size of the GeoGebra window as much as possible before exporting the construction as a dynamic worksheet called "TangentsCircle.html". Include a title and short explanations on what your students need to do when working with the interactive applets before saving the file.

Tip: You may want to use the tool "Move drawing pad" to drag your construction to the upper left corner of the graphics window. By using the tools "Zoom out" and "Zoom in" you are able to decrease or increase the size of your construction.

#### Second Applet

Now, we need to prepare the second interactive applet of this dynamic worksheet.

1. Open a new GeoGebra window.
2. Hide the algebra window and the axes by unchecking "Algebra window" as well as "Axes" in the menu "View".
3. Adjust the size of the GeoGebra window to give your students enough space to do their construction. Keep in mind, that the other applet needs to fit on screen too and that your students should be able to see both applets on one screen without scrolling.
4. Save the GeoGebra file as "GeoGebra_empty.ggb".
Tip: You don't need to export this "empty" construction as a dynamic worksheet.

After saving the ggb file you are ready to include the second interactive applet into your dynamic worksheet "TangentsCircle.html". Finally, you could use a customized tool bar in the second applet to simplify the construction process by limiting the number of available tools.