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6.1 Use Properties of TangentsPowerPoint Presentation

6.1 Use Properties of Tangents

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### 6.1Use Properties of Tangents

Vocabulary

- A circle is the set of all points in a plane that are equidistant from a given point called the center of the circle.
- A radius is a segment whose endpoints are the center and any point on the circle.

Vocabulary

- A chord is a segment whose endpoints are on a circle.
- A diameter is a chord that contains the center of the circle.
- The diameter is the longest chord a circle has.

Vocabulary

- A secant is a line that intersects a circle in two points.
- A tangent is a line in the plane of a circle that intersects the circle in exactly one point, the point of tangency.

Vocabulary

- Theorem 6.1:
- In a plane, a line is tangent to a circle if and only if the line is perpendicular to a radius of the circle at its endpoint on the circle.

Vocabulary

- Theorem 6.2:
- Tangent segments from a common external point are congruent.

Example 1:

- Tell whether the line, ray, or segment is best described as a radius, chord, diameter, secant, or tangent of circle P.

Example 2:

- Use the diagram to find the given lengths.

Example 3:

- Tell how many common tangents the circles have and draw them.

Example 4:

- RS is tangent to circle C at S and RT is tangent to circle C at T.
- Find the value of x.

Example 5:

- In the diagram, BC is a radius of circle C. Determine whether AB is tangent to circle C. Explain.

Example 6:

- In the diagram, B is a point of tangency. Find the radius r of circle C.

**Remember we know that the radius is perpendicular to the tangent**

This makes a RIGHT triangle!

So we can use Pythagorean theorem to solve for r.

Homework

P. 186 #1, 9-11, 12-20even

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