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Circumscribed Angles

Author:
Kim Hager
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Vocab Review

To circumnavigate 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 tangent to that circle.

In the applet above, which line(s) are tangent to the circle?

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Is there any way you can move the points so that these lines are not tangent to the circle?

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  • A
  • B
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What do you notice about the angle that the tangent lines make with the radii of the circle as you move the points?

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As you move point C in a clockwise direction toward B, what do you notice?

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What do you notice about the relationship between arc BC and arc BEC?

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What is the mathematical relationship between the arcs and the circumscribed angle?

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What do you notice about the length of the segments between the points of tangency and the vertex of the circumscribed angle?

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In the applet above, points B, C, D, and E are points of tangency. Name the pairs of segments that are congruent.

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In the applet above, points B, C, D, and E are points of tangency. Name the pairs of segments that are congruent.

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What do you wonder about the figures in the applets?

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