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