Circumscribed Angles
Vocab Review
To [u]circumnavigate[/u] means to travel around something. People circumnavigated the globe when they sailed around the world. When you circumscribe in geometry, you are drawing a figure around a circle without cutting into it. We say a line that meets a circle at only one point is called [u]tangent[/u] to that circle.
In the applet above, which line(s) are tangent to the circle?
Is there any way you can move the points so that these lines are not tangent to the circle?
What do you notice about the angle that the tangent lines make with the radii of the circle as you move the points?
As you move point C in a clockwise direction toward B, what do you notice?
What do you notice about the relationship between arc BC and arc BEC?
What is the mathematical relationship between the arcs and the circumscribed angle?
What do you notice about the length of the segments between the points of tangency and the vertex of the circumscribed angle?
In the applet above, points B, C, D, and E are points of tangency. Name the pairs of segments that are congruent.
In the applet above, points B, C, D, and E are points of tangency. Name the pairs of segments that are congruent.