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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

Chapter 10.1 Notes: Use Properties of Tangents

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

slide2

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.
slide3

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.
slide4

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.

slide5

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.

slide6

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

a. Radius of

b. Diameter of

c. Radius of

d. Diameter of

slide7

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.
slide8

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.

slide9

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

slide10

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.

slide11

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.

slide12

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

Ex.10: Is tangent to