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