Exploring Inscribed Angles

Instructions For Part 1

In the circle below, use the ray tool to create rays OB and OC, which creates a central angle. Use the angle measurement tool to measure . Then create rays AB and AC which creates an inscribed angle. Measure .
Now use the arrow tool tool to move around points A, B and/or C.

What do you notice is the relationship between the central angle () and the inscribed angle ()

Instructions for Part 2

Use the ray tool to create rays AB, AC, DB and DC. Use the angle measurement tool to measure and .

You can use the arrow tool to move the points around on the circle. What do you notice always seems to be true about and ?

Instructions for Part 3

On the circle below use the segment tool to create segments AB and AC. Use the angle measurement tool to measure angle CAB.

Use the arrow tool to move point A around on the circle. What do you notice is true about angle CAB?

Look back at your answer to Part 1. Explain why angle CAB has to be what it turned out to be.

So what kind of triangle is ABC?