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IM Geo.7.2 Lesson: Inscribed Angles

What do you notice? What do you wonder?

Use the applet to answer the questions. Do not show the angle measures until you are told to.

Name the central angle in this figure.

Name the inscribed angle in this figure.

Move point  around the circle. As you move this point, what happens to the measure of angle ? Show the angle measures to confirm.

Move points  and  to new positions. Record the measure of angles  and . Repeat this several times.

Make a conjecture about the relationship between an inscribed angle and the central angle that defines the same arc.

Here is a special case of an inscribed angle where one of the chords that defines the inscribed angle goes through the center.

The central angle  measures  degrees, and the inscribed angle  measures  degrees. Prove that .

The image shows a circle with chords CD, CB, ED, and EB. The highlighted arc from point C to point E measures 100 degrees. The highlighted arc from point D to point B measures 140 degrees.

Prove that triangles  and  are similar.