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 [math]\angle COB[/math]. Then create rays AB and AC which creates an inscribed angle. Measure [math]\angle CAB[/math].
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 ([math]\angle COB[/math]) and the inscribed angle ([math]\angle CAB[/math])
The inscribed angle is 1/2 of the measure of the central angle.[br]The central angle is twice the measure of the inscribed angle.
Use the ray tool to create rays AB, AC, DB and DC. Use the angle measurement tool to measure [math]\angle CAB[/math] and [math]\angle CDB[/math].
You can use the arrow tool to move the points around on the circle. What do you notice always seems to be true about [math]\angle CAB[/math] and [math]\angle CDB[/math]?
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?
It's always 90 degrees/right angle.
Look back at your answer to Part 1. Explain why angle CAB [i]has to be[/i] what it turned out to be.
Because it is half of 180 degrees (semicircle).
So what kind of triangle is ABC?