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Warm Up Write the equation of each item. 1. FG

Warm Up Write the equation of each item. 1. FG. x = –2. 2. EH. y = 3. 3. 2(25 – x ) = x + 2. 4. 3 x + 8 = 4 x. x = 16. x = 8. Objectives. Identify tangents, secants, and chords. Use properties of tangents to solve problems. Vocabulary.

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Warm Up Write the equation of each item. 1. FG

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  1. Warm Up Write the equation of each item. 1.FG x = –2 2.EH y = 3 3.2(25 –x) = x + 2 4. 3x + 8 = 4x x = 16 x = 8

  2. Objectives Identify tangents, secants, and chords. Use properties of tangents to solve problems.

  3. Vocabulary interior of a circle concentric circles exterior of a circle tangent circles chord common tangent secant tangent of a circle point of tangency congruent circles

  4. This photograph was taken 216 miles above Earth. From this altitude, it is easy to see the curvature of the horizon. Facts about circles can help us understand details about Earth. Recall that 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 circle with center C is called circle C, or C.

  5. ______________- the set of all points inside the circle. ______________- the set of all points outside the circle.

  6. Example 1: Identifying Lines and Segments That Intersect Circles Identify each line or segment that intersects L. chords: secant: tangent: diameter: radii:

  7. Example 2: Identifying Tangents of Circles Find the length of each radius. Identify the point of tangency and write the equation of the tangent line at this point. radius of R: radius of S: point of tangency: equation of tangent line:

  8. Example 2B Find the length of each radius. Identify the point of tangency and write the equation of the tangent line at this point. radius of C: 1 radius of D: 3 point of tangency: equation of tangent line:

  9. ____________- a line that is tangent to two circles.

  10. A common tangent is a line that is tangent to two circles.

  11. HK and HG are tangent to F. Find HG. Example 3A: Using Properties of Tangents

  12. RS and RT are tangent to Q. Find RS. Example 3B

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