Constructing a Tangent Line to a Circle

In this activity, you'll learn two different methods for constructing a tangent line from a point outside a circle to the circle.

Part A

You will first perform a construction using traditional tools.Watch this video aboutconstructing a tangent line to a circle.Use paper, a pencil, a compass, and a straightedge to perform the construction shown in the video. 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.

Font Sizes

Part B

You will now perform the construction of a tangent to a circle using modern tools.OpenGeoGebra, and complete each step below.If you need help, follow theseinstructionsfor using GeoGebra.

1. make the circle with a center at pointAwith a radius of your choice.
2. Now make the point outside of circleA, and label it pointB.Draw a line segment connecting pointsAandB.Find the midpoint of line segmentAB, and label it pointC.
3. Using pointCas the center, make the circle that passes through pointA.
4. CircleAand circleCintersect at two points.Find these intersection points, and label them pointsDandE.
5. Draw rays from pointBthrough pointDand from pointBthrough pointE.Also draw line segments connecting pointsAandDand pointsAandE.

Take a screenshot of your image, save it, and insert the image in the space provided.

Font Sizes

Part C

Look at the circle you created that has pointC(the midpoint of) as its center and passes through pointA.What can you say about, 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.

Font Sizes

Part D

What do the measures of anglesBDAandBEAand the fact thatandare radii of circleAtell us aboutandExplain your answer.

Font Sizes

Part E

Using the tools in GeoGebra, measureandto 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.

Font Sizes