Using Commands to Construct Tangents to a Circle
Task
As you saw in the last activity, the construction of tangents to a circle can be done by using geometric construction Tools only. You will now recreate this construction by just using keyboard input.
Construction steps
| 1. | A = (0, 0) | Create point A. Hint: The parentheses are closed automatically. |
| 2. | (0, 3) | Create point B. Hint: If you don’t specify a name objects are named in alphabetical order. |
| 3. | Circle(A,B) | Construct a circle c with center A through point B. Hint: This circle is a dependent object. |
Try it yourself...
Construction steps (continued)
| 4. | | Create point C. |
| 5. | s = Segment(A, C) | Create segment AC. |
| 6. | D = Midpoints(s) | Create midpoint D of segment AC. |
| 7. | d = Circle(D, C) | Construct a circle d with center D through point C. |
| 8. | Intersect(c, d) | Create intersection points E and F of the two circles c and d. |
| 9. | Line(C, E) | Create a tangent through points C and E. |
| 10. | Line(C, F) | Create a tangent through points C and F. |
Check and enhance your construction
- Perform the Drag Test in order to check if the construction is correct.
- Change the properties of the objects in order to improve the construction’s appearance using the
Style Bar (e.g. 
colors, 
line thickness, auxiliary objects 
dashed,...).
- Save the construction.
Hints
You can activate the 
Move Tool and double-click an object in the 
Algebra View in order to change its algebraic representation using the keyboard. Hit the Enter key once you are done.
Example: Change the coordinates of point B to B = (0, 4).
You may use the arrow keys in order to move Free Objects in a more controlled way. Activate the Move Tool and select an object (e.g. a free point) in either window. Press the up / down or left / right arrow keys in order to move the object into the desired direction.
Note: GeoGebra distinguishes between Free and Dependent Objects. While Free Objects can be directly modified either using the mouse or the keyboard, Dependent Objects adapt to changes of their parent objects. Thereby, it is irrelevant in which way (mouse or keyboard) an object was initially created.
Move Tool and double-click an object in the Algebra View in order to change its algebraic representation using the keyboard. Hit the Enter key once you are done.
Example: Change the coordinates of point B to B = (0, 4).
You may use the arrow keys in order to move Free Objects in a more controlled way. Activate the Move Tool and select an object (e.g. a free point) in either window. Press the up / down or left / right arrow keys in order to move the object into the desired direction.
Note: GeoGebra distinguishes between Free and Dependent Objects. While Free Objects can be directly modified either using the mouse or the keyboard, Dependent Objects adapt to changes of their parent objects. Thereby, it is irrelevant in which way (mouse or keyboard) an object was initially created.Suggestions for discussion
- Did any problems or difficulties occur during the construction steps?
- Which version of the construction (mouse or keyboard) do you prefer and why?
- Why should we use the keyboard for the input if we could also do it using Tools? Hint: There are Commands available that have no equivalent GraphicsTool.
- Does it matter in which way an object was created? Can it be changed in the Algebra View (using the keyboard) as well as in the
Graphics View (using the mouse)?