10b11ab Angles from Secants and Tangents
Suppose the entire pink arc measures 200 degrees and the entire blue arc measures 50 degrees. What would the measure of the manila angle be?
Move ANY ONE (just ONE -- doesn't matter which) of the PINK POINTS so the secant segment (for which this pink point is an endpoint) becomes TANGENT to the circle. Answer question #1 again within THIS CONTEXT.
Now move the pink points so that BOTH secant segments become TANGENT SEGMENTS. Suppose, in this case, the entire pink arc measures 200 degrees. What would the measure of the blue arc be? What would the measure of the manila angle be?
Next, move the MANILA POINT (outside the circle) as close to the circle as possible so that the blue arc almost disappears. (It won't disappear entirely). Keep the MANILA POINT on the circle. Now slowly re-slide the slider again. What previously learned theorem do these transformations reveal?
Suppose the 2 secant segments (drawn from the manila point outside the circle) intersect the circle above so that the manila angle measures 60 degrees and the entire pink arc measures 200 degrees. If this is the case, what would the measure of the entire blue arc be?