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Chapter 10.1 Notes: Use Properties of Tangents Goal: You will use properties of a tangent to a circle.

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Properties of a Circle 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 segment whose endpoints are on a circle. A diameter is a chord that contains the center of the circle.

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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, called the point of tangency.

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Ex.1: Tell whether the line, ray, or segment is best described as a radius, chord, diameter, secant, or tangent of a. b. c. d.

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Ex.2: Tell whether the line, ray, or segment is best described as a radius, chord, diameter, secant, or tangent of a. b. c. d.

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Ex.3: Use the diagram to find the given lengths. a. Radius of b. Diameter of c. Radius of d. Diameter of

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Properties of Tangents 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 circles.

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A line, ray, or segment that is tangent to two coplanar circles is called a common tangent. Ex.4: Tell how many common tangents the circles have and draw them. a. b. c.

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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. Ex.5: In the diagram, is a radius of Is tangent to

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Ex.6: In the diagram, B is a point of tangency. Find the radius of Theorem 10.2: Tangent segments from a common external point are congruent.

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Ex.7: is tangent to at S and is tangent to at T. Find the value of x. Ex.8: is tangent to Find the value of r.

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Ex.9: In is tangent at A and is tangent at B. Find x. Ex.10: Is tangent to

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Ex.11: Find the value of x.

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