A [b]secant line[/b] is a line that goes through the circle. This means that it intersects the circle in [b]two places[/b], kind of like an entrance and an exit.[br][br]The diagram below shows a circle with two secant lines. Take some time to move points B, C, D, and E around and watch the angle measures. [math]\alpha[/math] is the measure of arc CD, and [math]\beta[/math] is the measure of arc BE. [br][br]On the image below, you can press the play button to watch the construction happen. This is the order of steps:[br][br]1) Plot A - the center of the circle.[br]2) Plot B - a point on the circle.[br]3) Draw the circle through B with A as the center.[br]4) Plot C on the circle.[br]5) Connect B and C to make secant line BC.[br]6) Plot D on the circle.[br]7) Plot E on the circle.[br]8) Connect D and E to make secant line DE.[br]9). Measure arc CD [br]10). Measure arc BE[br]11). Plot F at the intersection of the secants.[br]12). Measure [math]\angle DFC[/math], the angle formed by the intersection of the secants.[br]

Take some time to move the points around that are on the circle. After you have moved them a little, set them with the following measurements and write down what the measure of angle DFC is in each situation.[br][br]Set the diagram so that arc CD = [math]96^{\circ}[/math] and arc BE = [math]70^\circ[/math]. What is the measure of [math]\angle DFC[/math]?[br][br][br]