In this section, you will investigate a special property of an inscribed angle that intercepts a semicircle, or 180° arc.

Create a table similar to the one shown below in your notes.

Using the applet, http://www.mathopenref.com/semiinscribed.html , move points A, B and C one at a time, noticing the angle measures. Write at least 4 entries in the table.

Journal Entry:

• Compare the angle measures, does the length of the diameter of the circle change the measure of the angle?  Explain.
• If B was the center of the circle instead of on the circle and the points A and B moved around the semicircle, what would be the measure of ∠ABC? What would the measure of arc AC be? Explain. 

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Check Your Answer

All of the angle measures are the same since B is inscribed with endpoints as the diameter for all the different diameters. The diameter is a straight line with a measure of 180 degrees, therefore the inscribed angle will always be 90 degrees. If B was the center of the circle, the angles would be central angle and both the central angle and the arc length would have the same measure, somewhere between 0 - 180°.)