CPM, Lesson 10.1.2, 10-15
INSCRIBED ANGLES
In the diagram below, is an example of an inscribed angle, because it lies within and its vertex lies on the circle. It corresponds to central because they both intercept the same arc, .
(An intercepted arc is an arc with endpoints on each side of the angle.)
Use the applet below to investigate part A.
PART A. In the circle below, , , and are examples of inscribed angles. Notice that all three angles intercept the same arc . Use the angle 
measurement tool to compare their measures. What do you notice?
measurement tool to compare their measures. What do you notice? Use the applet below to investigate part B.
PART B. Construct with the 
tool. Then, create the central angle and the inscribed angle using the point 
and segment 
tools. Compare the measures of these two angles.
Note: You can rename points by right clicking on them.
tool. Then, create the central angle and the inscribed angle using the point and segment tools. Compare the measures of these two angles.
Note: You can rename points by right clicking on them. Refer to your construction above
What is the relationship of an inscribed angle and its corresponding central angle? Is this observation true for all cases?