Angles in Circles

1. What do you notice about this diagram of circle O? Complete these statements about the angles:[br][math]\angle[/math]AOC is called a(n) ____________ angle because _______________________________________________.[br][math]\angle[/math]ABC is called a(n) ____________ angle because _______________________________________________.[br][br]2. Grab and move point C to several different locations. Make a conjecture about the angle measures.[br][br]3. Now grab and move point B. What do you notice about the angle measures?[br][br]4. Click in the checkbox to display the ratio of the measures of [math]\angle[/math]AOC and [math]\angle[/math]ABC. Grab and move points A, B, or C and observe.[br][br]5. What is the relationship between the types of angles shown in this diagram? Does it hold true for all locations of A, B, and C on the circle?[br][br]6. Move point B so that center O lies on the segment AB. Use this setup to prove your statement from #5.

Information: Angles in Circles