# Activities

• • • ##### Subject Area

• Math: Geometry: Circles

• ##### Author 9-12

15 Minutes

• ##### Device
• TI-84 Plus
• TI-84 Plus Silver Edition

TI Connect™

• ##### Accessories

TI Connectivity Cable
TI Keyboard

• ##### Report an Issue

Relationship Between Radius and Tangent to a Circle

#### Activity Overview

Generalize that a tangent and a radius form a 90-degree angle.

#### Before the Activity

Pair students and give them calculators.

#### During the Activity

1. Instruct students to draw a circle using the Cabri application.
2. Draw a line that does not intersect the circle.
3. Grab the line and move it until it intersects the circle at one point only.
4. Use the point tool to find intersection of circle and line.
5. Draw a segment from the intersection point to the center of the circle.
6. Measure the angle formed by the center of the circle (point A), the intersection (point B), and another point on the line.
7. What is the measure of the angle?
8. What is the measure of your partner's angle?
9. Erase the line and draw another in a different part of the plane. Repeat the process above and compare the measure of the angle formed between the radius and the tangent line.
10. What can you generalize about the measure of the angle formed by the radius of a circle and a line tangent to a circle?

#### After the Activity

After the activity the students should develop a logical proof that the radius is perpendicular to a tangent line. This proof may take many forms. Advanced students may use Cabri to construct a figure that will show the proof.