Constructing an Inscribed Equilateral Triangle + Activities

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.

The displayed line through is tangent to the circle at that point, and is a chord. Define the angle , reproduce the drawing on paper and draw an angle at the circumference congruent to , then the corresponding central angle.

Referring to the picture above, where the line through is tangent to the circle at that point, decide whether the following statements are true or false. If a statement is false, correct it to make it true, or provide a counterexample.

1. Angle subtends arc .
5. Angle is supplementary of angle

If a statement is false, correct it to make it true, or provide a counterexample.

1. If an angle at the circumference is acute, the corresponding central angle is obtuse.
2. The angles at the circumference that subtend the same arc or congruent arcs are congruent.