Which of these pizza slices gives the best value (the most pizza per dollar spent)?

Complete the table. Each row represents a circle with a defined sector.

Several circles with central angles are described. Select all the circles for which the central angle defines arcs that have length \(6\pi\) units.

Triangle \(ABC\) is shown with its incenter at \(D\). The inscribed circle’s radius measures 2 units. The length of \(AB\) is 9 units. The length of \(BC\) is 10 units. The length of \(AC\) is 17 units.

1. What is the area of triangle \(ABD\)?
2. What is the area of triangle \(BCD\)?

Noah makes three statements about the incenter of a triangle. 

1. To find the incenter of a triangle, all three angle bisectors must be constructed.
2. The incenter is always equidistant from the vertices of the triangle.
3. The incenter is always equidistant from each side of the triangle.

For each statement, decide whether you agree with Noah. Explain your reasoning.

Elena is writing notes about central angles in circles. Help her finish her notes by answering the questions.

1. Where is the vertex of a central angle located in relation to the circle?
2. What line segments related to circles are contained in the rays that form a central angle?
3. How does the measure of a central angle relate to the measure of the arc it is associated with?