 # 6.1 Use Properties of Tangents

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6.1 Use 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