Use compass and ruler to draw on paper the construction described in the app below.
The following app is the same as the previous one, but now includes GeoGebra tools.
Explore the entire construction in the app above, then use the GeoGebra tools to measure the sides of the hexagon and verify the construction numerically.[br][br](Use the [i]Undo [/i]and [i]Redo [/i]buttons at the top right of the toolbar, or refresh the browser page to delete possible objects you have created but that are not useful or correct).
Which circle is the hexagon inscribed in?[br][br]
Join each vertex of the hexagon with the center of the circle.[br]How many triangles do you obtain?[br]Prove that they are congruent to each other.[br][br]
What is the measure of the central angle that subtends the side of an inscribed regular hexagon?[br][br]
What is the measure of the corresponding angle at the circumference?[br][br]
The radius of a circle is [math]r=2[/math] in. [br]What is the length of the side of the regular hexagon inscribed in the circle?
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[/img][br][br][math]ABCDEF[/math] is an hexagon inscribed in a circle with radius [math]4[/math] in. [br]Using the data displayed in the figure above, can you say that [math]DC=2EF[/math]?[br][br]Verify your answer by calculating the lengths of the two sides.
If a statement is false, correct it to make it true, or provide a counterexample.[br][br]1. The center of the inscribed circle and circumscribed circle of a regular hexagon coincide.[br]2. Any hexagon can be inscribed in a circle.[br]3. All the sides of a circumscribed hexagon are inside the circle.[br]4. An hexagon is called [i]regular[/i] when all its sides are congruent and all its internal angles measure 60°.