# Properties of Tangents Drawn to Circles (VC)

- Author:
- Tim Brzezinski

## DIRECTIONS:

In the applet below, note the

**circle**with**center***You can alter the radius by dragging the***A**.**unlabeled point**on the circle.**Point***B*is a point on the circle.**Point**Feel free to alter the locations of any of these 4 points at any time. 1. Select the TANGENTS tool. Then select point*C*is a point that lies outside the circle.*B*and then select the circle. This will construct a line through*B*that is tangent to the circle. 2. Use the SEGMENT tool to construct radius . 3. Use the POINT ON OBJECT tool to plot a point*D*on this tangent line. Use the ANGLE tool to measure . (Be sure to select the points in this order.)4. Select the MOVE tool. Move point *B* around the circle. What do you notice?

5. Use the TANGENTS tool to construct a line passing through *C* that is tangent to the circle.
How many tangents can be drawn from point *C* to the circle?

6. Use the INTERSECT tool to plot the point(s) at which these tangents intersect the circle.
GeoGebra should name these points

*E*and*F*.7. Use the DISTANCE OR LENGTH tool to measure the distance from *C* to *E* and the distance from *C* to *F*. What do you notice?

8. What two new properties can we conclude about tangents drawn to circles? *Describe. *