Use Properties of Tangents Use properties of a

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. a) DC b) BD c) DE d) 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 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.

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 6. 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.