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nahimi
nahimi
23.04.2020 • 
Mathematics

Part A
You will first perform a construction using traditional tools. Watch this video about constructing a tangent line to a circle. Use paper, a pencil, a compass, and a straightedge to perform the construction shown in the video. In your own words, write the steps used for constructing tangent lines to a circle from a point outside the circle with only a compass and straightedge.

Part B
You will now perform the construction of a tangent to a circle using modern tools. Open GeoGebra, and complete each step below. If you need help, follow these instructions for using GeoGebra.
1.Create a circle with a center at point A with a radius of your choice.
2.Now create a point outside of circle A, and label it point B. Draw a line segment connecting points A and B. Find the midpoint of line segment AB, and label it point C.
3.Using point C as the center, create a circle that passes through point A.
4.Circle A and circle C intersect at two points. Find these intersection points, and label them points D and E.
5.Draw rays from point B through point D and from point B through point E. Also draw line segments connecting points A and D and points A and E.
Take a screenshot of your image, save it, and insert the image in the space provided.

Part C
Look at the circle you created that has point C (the midpoint of AB ) as its center and passes through point A. What can you say about AB ∠BCD ∠BEA, and the measures of those two angles? Use what you know about the inscribed angle of a circle, and include your reasoning in your response.

Part D
What do the measures of angles BDA and BEA and the fact that AD and AE are radii of circle A tell us about BD and BE Explain your answer.

Part E
Using the tools in GeoGebra, measure ∠BDA and ∠BEA to confirm the results found in part C. Take a screenshot of your image showing the angle measures, save it, and insert the image in the space provided.

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