Constructing an Inscribed Equilateral Triangle + Activities

Use compass and ruler to draw on paper the construction described in the app below.
Try It Yourself...
The following app is the same as the previous one, but now includes GeoGebra tools.
Verify with GeoGebra
Explore the entire construction in the app above, then use the GeoGebra tools to measure the sides of the triangle 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).
When is a polygon said to be inscribed in a circle?
When is a polygon said to be circumscribed about a circle?
What is the measure of the central angle that subtends the side of an inscribed regular triangle?
What is the measure of the corresponding angle at the circumference?
Referring to the construction above, explain why the triangle you obtain is equilateral.
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[/img][br]The displayed line through [math]A[/math] is tangent to the circle at that point, and [math]AB[/math] is a chord.[br]Define the angle [math]\alpha[/math], reproduce the drawing on paper and draw an angle at the circumference congruent to [math]\alpha[/math], then the corresponding central angle.
True or False?
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[/img][br][br]Referring to the picture above, where the line through [math]A[/math] is tangent to the circle at that point, decide whether the following statements are true or false.[br]If a statement is false, correct it to make it true, or provide a counterexample.[br][br][list=1][*]Angle [math]ABC[/math] subtends arc [math]ADC[/math].[/*][*][math]\angle BAD\cong\angle BCD[/math] [/*][*][math]\angle BAD\cong\alpha[/math] [/*][*][math]\angle BOD=2\angle BAD[/math] [/*][*]Angle [math]BAD[/math] is supplementary of angle [math]BCD[/math][br][/*][/list]
True or False?
If a statement is false, correct it to make it true, or provide a counterexample.[br][br][list=1][*]If an angle at the circumference is acute, the corresponding central angle is obtuse.[/*][*]The angles at the circumference that subtend the same arc or congruent arcs are congruent.[br][/*][/list]
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Information: Constructing an Inscribed Equilateral Triangle + Activities