Exercise 10 Page 534

Before naming a tangent and a point of tangency from the graph, let's review some important definitions about circles.

• Radius: A segment whose endpoints are the center and any point on the circumference on a circle.
• Chord: A segment whose endpoints are on the circumference of a circle.
• Diameter: A chord that contains the center of the circle.
• Secant: A line that intersects a circle in two points.
• Tangent: A line in the plane of a circle that intersects the circle in exactly one point — the point of tangency.

Now, consider the given diagram. We can see that $\overleftrightarrow{GE}$ intersects the circle in exactly one point.

Therefore, according to the definitions, $\overleftrightarrow{GE}$ is a tangent to the circle. Note that, this is only one of the many names this line can take. Additionally, $F$ is the point of tangency.