In this part of the lesson, you will investigate the relationship between the measure of an inscribed angle and its corresponding central angle.

Explore the relationship between the measure of an inscribed angle and its corresponding central angle. First, create a table similar to the one below in your notes.

m∠AOB = m	m∠APB

Using the interactive applet, http://www.mathopenref.com/arccentralangletheorem.html, move points A, B and P around the circle one at a time, compare the two angle measures and write down at least 4 entries in the table.

Journal Entry:

Both angle measures were provided, compare the angle measures to the arc measure.  Would the angle measures and arc measures change if the radius of the circle changed? 

Interactive popup. Assistance may be required.

Check Your Answer

The arc measure was the same for both angles but the central angle was always equal to the arc measure and twice or 2 times the measure of the inscribed angle. The angles and arc measures would NOT change if the radius of the circle changed because the central angle is always between 0 - 360 degrees, therefore the measure of the arc would be between 0 – 360 degrees and the inscribed angle would be half of the measure of the central angle or arc.