10.1 Use Properties of Tangents Use properties of a tangent to a circle

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 segment whose endpoints are the center and any point on the circle is a radius. A chord is a line segment that intersects a circle in two points. The diameter of a circle is a chord that goes through the center of the circle.

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.

Example 1: Tell whether the line or segment is best described as a radius, chord, diameter, secant, or tangent of circle C. DC BD DE AE

Example 2

Coplanar Circles Two circles can intersect in two points, one point, or no points. Coplanar Circles that intersect in one point are called tangent circles. Coplanar circles that have a common center are called concentric

Common Tangents A line, ray, or segment that is tangent to two coplanar circles is called a common tangent.

Example 3: Draw common Tangents Tell how many common tangents the circles have.

Theorem 10.1 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.

Example 4: In the diagram, AB is a radius of circle A. Is BC tangent to circle A. Explain.

Example 5: In the diagram, S is a point of tangency. Find the radius of r of circle T.

Theorem 10.2: Tangent segments from a common external point are congruent

Example 6: Use properties of tangents. In circle C, DA, is tangent at A and DB is tangent at B. Find x.

 Homework  Pg 655/1-10,12-17,27,28,35,36