Secants: In and Out
Explore how the angle formed by two secants of a circle relates to the intercepted arc(s).
There are three situations that we explored:
1) the secants intersect on the circle (vertex of the angle lies on the circle);
2) the secants intersect inside the circle;
3) the secants intersect outside the circle.
For each case is simple discussion relating the measure of angle ABC and the intercepted arc(s).
In exploring the location of point A, where the secants intersect, I discovered that there was a “number line” effect :
Negative (subtract) Zero Positive (add)
When A is outside the circle, you subtract the intercepted arcs and take half, when A is on the circle you just take half of the intercepted arc and when A is inside the circle you add the intercepted arcs and take half.
Click here to view the GSP file where you can further explore the location of A.