Using Properties of Tangents to Solve for Unknown Lengths

Objective:  Have students work with properties of tangents of circles to help them better understand the theorems discovered the previous day.

Lesson:  Have students work through an activity that will help them better understand the theorems concerning properties of tangent lines and secant lines in circles.

Daniel needs to figure out the amount of grain that is held in a silo. Before he can do so, he must know the radius of the silo. He currently knows that when he is standing approximately 8 feet away from the silo he is approximately 16 feet away from a point of tangency of the silo.

Before we investigate this problem further, let's look at a few example problems that might aid us in our investigation.

Given the diagrams below, find the unknown lengths. Show all work.

Now try drawing a diagram for the given problem.

Now, how might you use what you know about tangents of circles to go about solving this problem?

What is the length of the radius of the silo? Show your work.