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Inscribed Angles (Angles on a Circles Edge)

The pink angle is said to be an inscribed angle within the circle below. This inscribed angle intercepts the thick blue arc of the circle. Because of this, this thick blue arc is said to be the inscribed angle's intercepted arc. Notice how the blue central angle also intercepts this same thick blue arc. To start: 1) Move point D wherever you'd like. 2) Adjust the size of the thick blue intercepted arc by moving the other 2 blue points (if you wish.) 3) Click the checkbox to lock point D. 4) Follow the interactive prompts that will appear in the applet. Interact with the following applet for a few minutes. Then, answer the questions that follow.

How many pink inscribed angles fill a central angle that intercepts the same arc? What does this tell you about the relationship between a central angle and an inscribed angle?

Slide the gray tool to the right and notice what happens. Change the length of the blue intercepted arc and see what happens to the measures of the pink inscribed angles.

What does this second activity tell us about the relationship between all inscribed angles and the central angle that share the same arc?

Play with the app to discover the relationship between opposite angles in an inscribed quadrilateral in a circle.

What can you say about the measure of opposite angles in an inscribed quadrilateral?