Presentation on theme: "10.1 Use Properties of Tangents"— Presentation transcript:
1 10.1 Use Properties of Tangents Use properties of a tangent to a circle
2 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.
3 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.
4 Example 1:Tell whether the line or segment is best described as a radius, chord, diameter, secant, or tangent of circle C.DCBDDEAE
6 Coplanar CirclesTwo 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
7 Common TangentsA line, ray, or segment that is tangent to two coplanar circles is called a common tangent.
8 Example 3: Draw common Tangents Tell how many common tangents the circles have.
9 Theorem 10.1In 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.
10 Example 4:In the diagram, AB is a radius of circle A. Is BC tangent to circle A. Explain.
11 Example 5:In the diagram, S is a point of tangency. Find the radius of r of circle T.
12 Theorem 10.2:Tangent segments from a common external point are congruent
13 Example 6: Use properties of tangents. In circle C, DA, is tangent at A and DB is tangent at B. Find x.