[size=100]As you saw in the last activity, the construction of tangents to a circle can be done by using geometric construction [i]Tools [/i]only. You will now recreate this construction by just using keyboard input.[/size]

[table] [tr] [td][size=100]1.[/size][/td] [td][font=Courier New][size=100]A = (0, 0)[br][/size][/font][/td] [td][size=100]Create point [i]A[/i].[br][u]Hint[/u]: The parentheses are closed automatically.[/size][/td][/tr] [tr] [td][size=100]2.[/size][/td] [td][font=Courier New][size=100](0, 3)[br][/size][/font][/td] [td][size=100]Create point [i]B[/i].[br][u]Hint[/u]: If you don’t specify a name objects are named in alphabetical order.[/size][/td][/tr][tr] [td][size=100]3.[/size][/td] [td][font=Courier New][size=100]Circle(A,B)[br][/size][/font][/td] [td][size=100]Construct a circle [i]c[/i] with center [i]A[/i] through point [i]B[/i].[br][u]Hint[/u]: This circle is a dependent object.[/size][/td][/tr][/table]

[table] [tr] [td][size=100]4.[/size][/td] [td][size=100][font=Courier New][code][/code][/font][font=Courier New]C = (5,4)[/font][br][/size][/td] [td][size=100]Create point [i]C[/i].[/size][/td][/tr] [tr] [td][size=100]5.[/size][/td] [td][size=100][font=Courier New]s = Segment(A, C)[/font][br][br][/size][/td] [td][size=100]Create segment [i]AC[/i].[/size][/td][/tr] [tr] [td][size=100]6.[/size][/td] [td][size=100][font=Courier New]D = Midpoints(s)[/font][br][/size][/td] [td][size=100]Create midpoint [i]D[/i] of segment [i]AC[/i].[/size][/td][/tr] [tr] [td][size=100]7.[/size][/td] [td][size=100][font=Courier New]d = Circle(D, C)[/font][br][/size][/td] [td][size=100]Construct a circle [i]d[/i] with center [i]D[/i] through point [i]C[/i].[/size][/td][/tr] [tr] [td][size=100]8.[/size][/td] [td][size=100][font=Courier New]Intersect(c, d)[/font][br][br][/size][/td] [td][size=100]Create intersection points [i]E[/i] and [i]F[/i] of the two circles [i]c[/i] and [i]d[/i].[/size][/td][/tr] [tr] [td][size=100]9.[/size][/td] [td][font=Courier New][size=100]Line(C, E)[/size][/font][/td] [td][size=100]Create a tangent through points [i]C[/i] and [i]E[/i].[/size][/td][/tr] [tr] [td][size=100]10.[/size][/td] [td][size=100][font=Courier New]Line(C, F)[/font][br][/size][/td] [td][size=100]Create a tangent through points [i]C[/i] and [i]F[/i].[/size][/td][/tr][/table][size=100][br][/size]

[list][*][size=100] Perform the Drag Test in order to check if the construction is correct.[br][/size][/*][*][size=100] Change the properties of the objects in order to improve the construction’s appearance using the [img]https://wiki.geogebra.org/uploads/thumb/d/db/Stylingbar_icon_graphics.svg/16px-Stylingbar_icon_graphics.svg.png[/img] [i]Style Bar[/i] (e.g. [img]https://wiki.geogebra.org/uploads/thumb/f/ff/Stylingbar_color_blue.svg/16px-Stylingbar_color_blue.svg.png[/img] colors, [img]https://wiki.geogebra.org/uploads/thumb/3/3d/Stylingbar_line_solid.svg/16px-Stylingbar_line_solid.svg.png[/img] line thickness, auxiliary objects [img]https://wiki.geogebra.org/uploads/thumb/d/db/Stylingbar_line_dashed_short.svg/16px-Stylingbar_line_dashed_short.svg.png[/img] dashed,...).[br][/size][/*][*][size=100] Save the construction.[/size][/*][/list]

[size=100]You can activate the [img]https://wiki.geogebra.org/uploads/thumb/8/83/Mode_move.svg/16px-Mode_move.svg.png[/img] [i]Move[/i] Tool and double-click an object in the [size=100][img]https://wiki.geogebra.org/uploads/thumb/4/40/Menu_view_algebra.svg/16px-Menu_view_algebra.svg.png[/img][/size] [i]Algebra View[/i] in order to change its algebraic representation using the keyboard. Hit the [i]Enter[/i] key once you are done.[br][u]Example[/u]: Change the coordinates of point [i]B[/i] to [font=Courier New]B = (0, 4)[/font].[br][br]You may use the arrow keys in order to move Free Objects in a more controlled way. Activate the [size=100][img]https://wiki.geogebra.org/uploads/thumb/8/83/Mode_move.svg/16px-Mode_move.svg.png[/img][/size] [i]Move[/i] 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.[br][br][u]Note[/u]: GeoGebra distinguishes between [b]Free [/b]and [b]Dependent Objects[/b]. 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.[/size]

[list][*][size=100] Did any problems or difficulties occur during the construction steps?[br][/size][/*][*][size=100] Which version of the construction (mouse or keyboard) do you prefer and why?[br][/size][/*][*][size=100] Why should we use the keyboard for the input if we could also do it using [i]Tools[/i]?[br][u]Hint[/u]: There are [i]Commands [/i]available that have no equivalent [i]GraphicsTool[/i].[br][/size][/*][*][size=100] Does it matter in which way an object was created? Can it be changed in the [img]https://wiki.geogebra.org/uploads/thumb/4/40/Menu_view_algebra.svg/16px-Menu_view_algebra.svg.png[/img] [i]Algebra View[/i] (using the keyboard) as well as in the [img]https://wiki.geogebra.org/uploads/thumb/c/c8/Menu_view_graphics.svg/16px-Menu_view_graphics.svg.png[/img] [i]Graphics View[/i] (using the mouse)?[/size][/*][/list]