# Angles from Secants and Tangents (V1)

**BIG POINTS**each time

*before*you slide the slider.

## 1.

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?
**

## 2.

**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.

## 3.

Now **m****ove 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? **

## 4.

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?

## 5.

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**?