This is an investigation to determine the relationship between a central angle and an inscribed angle.[br][br]The points on the circle and the radius are dynamic and can be moved.

1. Write down the measure of the arc in the given table. Click the box next to Central angle in the above activity and write that measure in the appropriate spot on the given table. Now click the box next to inscribed angle above and record its measure in the table. [br][br]2. Now un-click the boxes next to central angle and inscribed angle and then Click on point B above and while holding the cursor down move point B around the circle so that the red arc is smaller than the red arc measure in step one. Record this new arc measure in the table. Make a guess at the new measures of the central angle , angle BAC, and inscribed angle , angle BDC. Now click the boxes next to Central and Inscribed above. Record these measures on the table. Did you make good guesses? Move point D. How does this change the inscribed angle measure?[br][br]3. Move point B again so the red arc is 180 degrees Record the measures of the arc, central angle and inscribed angle on the table. Does changing the radius change the angle measures?[br][br]4. , Looking at your table, make an observation (and record it in the table) about the relationship between the central angle (BAC) and the arc measure?[br][br]5. One more test Move point B one more time so that the red arc measures more than 180 degrees. Record the measures in the table. [br][br]6. What is the relationship between the inscribed angle (BDC) and the arc measure? Is this the same relationship between the inscribed angle and central angle?