Presentation on theme: "10.1 Use Properties of Tangents Use properties of a tangent to a circle."— Presentation transcript:
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. a)DC b)BD c)DE d)AE
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.