Chapter 10.5 Notes: Apply Other Angle Relationships in Circles

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Chapter 10.5 Notes Apply Other Angle
Relationships in Circles

• Goal You will find the measures of angles inside
  or outside a circle.

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• How do you find the measure of an inscribed
  angle?
• Theorem 10.11
• If a tangent and a chord intersect at a point on
  a circle, then the measure of each angle formed
  is one half the measure of its intercepted arc.

3

• Ex.1 Line m is tangent to the circle. Find the
  measure of the red angle or arc.
• Line m is tangent to the circle. Find x or y.
• Ex.2 Ex.3

4

• Intersecting Lines and Circles
• If two lines intersect a circle, they intersect
  in three places.
• Theorem 10.12 Angles Inside the Circle Theorem
• If two chords intersect inside a circle, then
  the measure of each angle is one half the sum of
  the measures of the arcs intercepted by the angle
  and its vertical angle.

5

• Ex.4 Find the value of x.
• Ex.5 Find the value of x.

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• Theorem 10.13 Angles Outside the Circle Theorem
• If a tangent and a secant, two tangents, or two
  secants intersect outside a circle, then the
  measure of the angle formed is one half the
  difference of the measures of the intercepted
  arcs.
• Ex.6 Find the value of x.

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• Find the value of the variable.
• Ex.7 Ex.8
• Ex.9 Ex.10