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

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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.

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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.

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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

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Example 2

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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

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

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

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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.

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

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

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

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

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

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