Chapter 10.1 Notes: Use Properties of Tangents

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

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### Chapter 10.1 Notes: Use Properties of Tangents

Goal: You will use properties of a tangent to a circle.

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.

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.

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.

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.

Ex.3: Use the diagram to find the given lengths.

b. Diameter of

d. Diameter of

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.

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.

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

• Theorem 10.2:

Tangent segments from a common external point are congruent.

at T. Find the value of x.

Ex.8: is tangent to Find the value of r.

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

Ex.10: Is tangent to