Working with another student is recommended. Please list his name here: ___________________ However, the words you write must be your own. NO COPYING! It is an honor offense to copy someone else’s words and pass them off as your own. Even if you work together and come up with a "shared wording" that both of you write down, that is not the same as writing your own words and would be considered an honor offense. Please initial here to indicate that you understand that the words you write must be your own: _______

1. Open a new sketch. Using the circle tool, place a circle on the sketch.

Select the circle, and use CONSTRUCT POINT ON OBJECT to place another point on the circle.

Label the points on the circle A and B. Label the center of the circle O.

Construct the segments sOA and sOB.

Raise your hand so that I may check your work. Mr. Hansen’s initials: ____________

mÐAOB = _____________

Select this measure, and use CALCULATE to find the ratio of the measure of ÐAOB to 360 degrees. (You may need to use the UNITS function of the Sketchpad calculator to label the 360 as 360°. Give your answer, as always, to 3 decimal places.)

ratio = ____________

2. Now select only the circle, and use MEASURE to find the circumference of the circle. C = _______________

Select the circle and the points A and B. Be careful not to change the radius of the circle in the following steps.

Use MEASURE to find ARC LENGTH and ARC ANGLE.

Arc length = ______________ Arc measure (degrees) = ______________

Select Circumference and Arc-Length. Use CALCULATE to find the ratio of arc-length to circumference.

ratio = ____________

3. Move point B around on the circle until Ð AOB has measure equal to each of the measures in the following table. Record the information required in the table. Fill in the last row with a random value of your choice between 45 and 90. (Do not use 60 a second time.)

4. Answer these questions.

a) What is the "Arc-Angle" which sketchpad measured and called either "mÐ arc BA on circle OB" or "mÐ arc AB on circle OB"? Hint: Is it a central Ð or an inscribed Ð , or some other type of Ð ? If so, what is its name?

___________________________________________________________

b) For part (b), assume that you know the length of the radius of a circle. In this and all similar questions, be sure to define all variables clearly.

c) Let Ð AOB be an acute central angle in circle O. Provide a diagram and write a rule or formula for finding the area of sector AOB.

d) Repeat part (c), except this time give a rule or formula for finding the area of the "Pac-Man" shaped region that is the portion of the circle not represented by sector AOB.

1. Open a new sketch. Using the circle tool, place a circle on the sketch.

Select the circle, and use CONSTRUCT POINT ON OBJECT to place two more points on the circle.

Label the points on the circle A, B, and C. Label the center of the circle O.

Construct the chords sAB and sBC. An angle like ÐABC with its vertex on the circle and sides that contain chords is called a(n) ______________________ angle, and ________________ is called the intercepted arc of ÐABC. Call me over (Mr. Hansen's initials: _________ ) or attach a printout so that I can see your work.

2. Measure angle ABC. mÐ ABC = _______________

Select point A, point C, and the circle. Use Sketchpad to measure minor arc AC: _____________.

3. Move the points around on the circle so that ÐABC has various measures. Complete the table below.

4. Write a conjecture or conjectures relating the measure of an inscribed angle to the measure of its intercepted minor arc. Use careful, accurate wording, good grammar, and one or more complete sentences.