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Big Ideas Math Geometry, 2014

BI

Big Ideas Math Geometry, 2014 View details

1. Lines and Segments That Intersect Circles

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Exercise 35 Page 535

Note that a tangent is a line that intersects a circle at exactly one point.

See solution.

Practice makes perfect

Let's begin by recalling the definition of a tangent line to a circle.

A tangent is a line in the plane of a circle that intersects the circle at exactly one point. This point is called the point of tangency.

Let's draw a diagram to visualized the definition.

We will investigate the number of tangent lines to a circle that pass through the following points.

A point outside the circle
A point on the circle
A point inside the circle

Let's do it!

Point Outside of the Circle

We will first draw a circle and locate an exterior point.

Next, we will draw lines such that they pass through A and intersect the circle at exactly one point.

As we can see, there are two lines that are tangent to the circle and pass through an exterior point.

Point on the Circle

This time, we will locate the point on the circle.

The point on the circle is the point of tangency of the tangent line.

Therefore, we have only one tangent line that passes through a point on the circle.

Point Inside the Circle

Finally, we will locate the point inside the circle.

No matter how we draw the lines, if they pass through A, they will always intersect the circle at two points.

Therefore, there is not a tangent line that passes through a point inside the circle.

Subchapter links

Communicate Your Answer p.529

Monitoring Progress p.530-533