Secant Lines - Intersect in the Circle
What is a Secant Line?
A secant line is a line that goes through the circle. This means that it intersects the circle in two places, kind of like an entrance and an exit.
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. is the measure of arc CD, and is the measure of arc BE.
On the image below, you can press the play button to watch the construction happen. This is the order of steps:
1) Plot A - the center of the circle.
2) Plot B - a point on the circle.
3) Draw the circle through B with A as the center.
4) Plot C on the circle.
5) Connect B and C to make secant line BC.
6) Plot D on the circle.
7) Plot E on the circle.
8) Connect D and E to make secant line DE.
9). Measure arc CD
10). Measure arc BE
11). Plot F at the intersection of the secants.
12). Measure , the angle formed by the intersection of the secants.
Constructing Two Secants
Move the points...
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.
Set the diagram so that arc CD = and arc BE = . What is the measure of ?
Set the diagrams so that arc CD is 40 degrees and arc BE is 100 degrees. 1. What is the sum of the two arcs? 2. What is the measure of angle DFC now?
Set the diagram so that arc CD is 28 degrees and arc BE is 52 degrees. 1. What is the sum of the two arcs? 2. What is the measure of angle DFC now?
Last one... set the diagram so that arc CD is 110 degrees and arc BE is 70 degrees. 1. What is the sum of the two arcs? 2. What is the measure of angle DFC now?
Pattern?
Did you notice a pattern in the angles that you found? If you can describe it in an equation, try to do that!