The following applet shows a quadrilateral that has been inscribed in a circle. [br][br]Recall what you've learned form the INSCRIBED ANGLE THEOREM (http://tube.geogebra.org/b/1457199#material/1473237). [br]This will help you discover yet a new corollary to this theorem.[br][br]Notice how the measures of angles [color=#1551b5]A[/color] and [color=#b20ea8]C[/color] are shown. (A and C are [b]opposite angles[/b] of a cyclic quadrilateral.) Complete the following: [br][br]1) How does the measure of angle [color=#1551b5]A[/color] compare with the measure of [color=#1551b5]arc BCD[/color]? Why is this?[br]2) How does the measure of angle [color=#b20ea8]C[/color] compare with the measure of [color=#b20ea8]arc BAD[/color]? Why is this?[br]3) What is the sum of the measures of arcs [color=#1551b5]BCD[/color] & [color=#b20ea8]BAD[/color]? (This one's easy!)[br]4) According to your answers for (1), (2), & (3), what should the sum of the measures of angles [color=#1551b5]A[/color] & [color=#b20ea8]C[/color] be? [br]5) Confirm your answer to (4) by clicking the checkbox in the lower right hand corner. (Be sure to move points B and [color=#0a971e]D[/color] around after doing so!) [br][br]6) Click on the "Show measures of angles B & D" checkbox now.[br]7) How does the measure of angle B compare with the measure of arc ADC? Why is this?[br]8) How does the measure of angle [color=#0a971e]D[/color] compare with the measure of [color=#0a971e]arc ABC[/color]? Why is this?[br]9) What is the sum of the measures of arcs ADC & [color=#0a971e]ABC[/color]? (This one's easy!)[br]10) According to your answers for (7), (8), & (9), what should the sum of the measures of angles B & [color=#0a971e]D[/color] be? [br]11) Confirm your answer to (10) by clicking the checkbox in the lower right hand corner. (Be sure to move points [color=#1551b5]A[/color] and [color=#b20ea8]C[/color] around after doing so!) [br][br][b]Complete the following corollary: If a quadrilateral is inscribed in a circle, then both pairs of opposite angles are...[/b]

Questions are located above the applet.