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G.GCI.3 Cyclic Quadrilaterals

Any quadrilateral that is inscribed inside a circle is said to be a cyclic quadrilateral. In the applet below, a cyclic quadrilateral (with moveable vertices) is shown. Slide the slider slowly and carefully observe what happens. Then, reset the applet. Change the locations of the BIG POINTS and repeat this process. Repeat the previous steps a few more times. Then, answer the questions that follow.


Suppose, in the applet above, the brown angle measures 76 degrees. What would the measure of the blue angle be?


Suppose, in the applet above, the pink angle measures 130 degrees. What would the measure of the green angle be?


From what you've observed, how would you describe the relationship between any pair of opposite angles of a cyclic quadrilateral?


Note that all 4 of this cyclic quadrilateral's interior angles are inscribed angles of a circle. How does the measure of an inscribed angle compare with the measure of the arc (of the circle) it intercepts?


Explain why, using your response for (4) above, the phenomena you've observed above holds true for any cyclic quadrilateral.