Tangent Lines to Circles
Let's look at a few example problems.
This proof relies on the fact that the shortest distance from a point to a line is along the segment perpendicular to the line.
In general, the angle between two lines tangent to a circle from the same point will be supplementary to the central angle created by the two tangent lines.
Earlier, you were given a problem about tangent lines to a circle.
In the following questions, you will learn how to construct lines tangent to a circle from a given point.
1. What is a tangent line?
For all pictures below, assume that lines that appear tangent are tangent.
Use the image below for #2-#3.
Use the image below for #4-#7.
Use the image below for #8-#9.
Use the image below for #10-#11. 62% of the circle is purple.
10. Find the measure of the purple arc.
Use the image below for #12-#13.
13. Prove your conjecture from #12.
14. Use construction tools of your choice to construct a circle and a point not on the circle. Then, construct two lines tangent to the circle that pass through the point. Hint: Look at the Guided Practice questions for the steps for this construction.
15. Justify why your construction from #14 created tangent lines.
To see the Review answers, open this PDF file and look for section 8.7.