Angles Outside the Circle

Topic:
Geometry

Angles formed by Secant Lines

Secant lines intersect a circle at two points. Activity Directions: Move points D, C, B, and E to discover the relationship between the measure of the angle created by two secant lines and the measures of the intercepted arcs.

What happens if you add arc CB and arc DE?

What happens in you subtract arc CB from arc DE?

Do you see a relationship between either the sum of the 2 arcs or a relationship between the difference in the arcs? If so, what do you notice?

What happens if you have a secant and a tangent?

Click on A and move it around the circle. Determine the measure Arc AB. Determine the measure of arc DE. Try to figure out the relationship between the 2 arcs and the angle.

What happens if you add arc AB and arc DE?

What happens in you subtract arc DE from arc AB?

Do you see a relationship between either the sum of the 2 arcs or a relationship between the difference in the arcs? If so, what do you notice?

What happens if you have 2 tangent lines? Move point B around the circle.

What's the measure of arc BFC?

What's the measure of arc CB?

How many arcs are present when you have 2 tangent lines?

What happens when you add the 2 angles together?

Do you see a relationship between the two arcs and the angle created by the tangents?