[size=100]Summarize the properties of a regular hexagon before you start your actual construction. [br][br][u]Hint[/u]: If you are not familiar with the construction steps necessary for a regular hexagon construction, you might want to explore the applet below. Just use the buttons of the [i]Navigation[/i][i] Bar[/i] in order to replay the construction steps. [/size]

[size=100]Construct a regular hexagon that passes the drag test by following the construction steps provided below.[/size]

[table][tr][td][size=100]1.[/size][/td][td][size=100][icon]https://tube.geogebra.org/images/ggb/toolbar/mode_circle2.png[/icon][/size][/td][td][size=100]Draw a circle [i]c[/i] with center [i]A[/i] through point [i]B[/i].[/size][/td][td][/td][td][size=100]7.[/size][/td][td][size=100][icon]https://tube.geogebra.org/images/ggb/toolbar/mode_intersect.png[/icon][/size][/td][td][size=100]Intersect the new circle [i]f[/i] with circle [i]c[/i] in order to get vertex [i]F[/i].[/size][/td][/tr][tr][td][size=100]2.[/size][/td][td][size=100][icon]https://tube.geogebra.org/images/ggb/toolbar/mode_circle2.png[/icon][/size][/td][td][size=100]Construct a new circle [i]d[/i] with center [i]B[/i] through point [i]A[/i].[/size][/td][td][/td][td][size=100]8.[/size][/td][td][size=100][icon]https://tube.geogebra.org/images/ggb/toolbar/mode_circle2.png[/icon][/size][/td][td][size=100]Construct a new circle [i]g[/i] with center [i]E[/i] through point [i]A[/i].[/size][/td][/tr][tr][td][size=100]3.[/size][/td][td][size=100][icon]https://tube.geogebra.org/images/ggb/toolbar/mode_intersect.png[/icon][/size][/td][td][size=100]Intersect the circles [i]c[/i] and [i]d[/i] to get the hexagon’s vertices [i]C[/i] and [i]D[/i].[br][/size][/td][td][/td][td][size=100]9.[/size][/td][td][size=100][icon]https://tube.geogebra.org/images/ggb/toolbar/mode_intersect.png[/icon][/size][/td][td][size=100]Intersect the new circle [i]g[/i] with circle [i]c[/i] in order to get vertex [i]G[/i].[/size][/td][/tr][tr][td][size=100][/size][/td][td][size=100][/size][/td][td][size=100][u]Hint:[/u] Selecting circle [i]d[/i] and circle [i]c[/i] creates both intersection points. [/size][/td][td][/td][td][size=100]10.[br][/size][/td][td][size=100][icon]https://tube.geogebra.org/images/ggb/toolbar/mode_polygon.png[/icon][/size][/td][td][size=100]Draw a hexagon in counter-clockwise orientation using the intersection points of the circles.[br][/size][/td][/tr][tr][td][size=100]4.[/size][/td][td][size=100][icon]https://tube.geogebra.org/images/ggb/toolbar/mode_circle2.png[/icon][/size][/td][td][size=100]Construct a new circle [i]e[/i] with center [i]C[/i] through point [i]A[/i].[/size][/td][td][/td][td][size=100]11.[br][/size][/td][td][size=100][icon]https://tube.geogebra.org/images/ggb/toolbar/mode_showhideobject.png[/icon][/size][/td][td][size=100]Hide the circles.[br][/size][/td][/tr][tr][td][size=100]5.[/size][/td][td][size=100][icon]https://tube.geogebra.org/images/ggb/toolbar/mode_intersect.png[/icon][/size][/td][td][size=100]Intersect the new circle [i]e[/i] with circle [i]c[/i] in order to get vertex [i]E[/i].[/size][/td][td][/td][td][size=100]12.[/size][/td][td][size=100][icon]https://tube.geogebra.org/images/ggb/toolbar/mode_angle.png[/icon][/size][/td][td][size=100]Display the interior angles of the hexagon.[/size][/td][/tr][tr][td][size=100][/size][/td][td][size=100][/size][/td][td][size=100][u]Hint:[/u] If you just want a single intersection point, [br]click directly on the intersection of the two circles.[/size][/td][td][/td][td][size=100][br][/size][/td][td][size=100][/size][/td][td][size=100][u]Hint[/u]: If you get the exterior angles, you probably created the hexagon in clockwise orientation.[/size][/td][/tr][tr][td][size=100]6.[/size][/td][td][size=100][icon]https://tube.geogebra.org/images/ggb/toolbar/mode_circle2.png[/icon][/size][/td][td][size=100]Construct a new circle [i]f[/i] with center [i]D[/i] through point [i]A[/i].[/size][/td][td][/td][td][size=100]13.[/size][/td][td][size=100][icon]https://tube.geogebra.org/images/ggb/toolbar/mode_move.png[/icon][/size][/td][td][size=100]Perform the drag test to check if your construction is correct.[/size][/td][/tr][/table][size=100][u][br]Hint[/u]: You might want to [url=https://tube.geogebra.org/student/bnJrQAIj2#material/688533]save your construction[/url] using the [i]File [/i]menu.[/size]

[size=100]Try to find an explanation for this construction process.[br][u]Hint[/u]: Which radius do the circles have and why?[/size]