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1 Lesson 10-5 Apply Other Angle Relationships in Circles.

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Presentation on theme: "1 Lesson 10-5 Apply Other Angle Relationships in Circles."— Presentation transcript:

1 1 Lesson 10-5 Apply Other Angle Relationships in Circles

2 2 Angles Inside the Circle Theorem (Interior Angle Theorem) Angles that are formed by two intersecting chords.Definition: The measure of the angle formed by the two intersecting chords is equal to ½ the sum of the measures of the intercepted arcs. Interior Angle Theorem: 1 A B C D E 2

3 3 A B C D x°x° 91  85  Example: Interior Angle Theorem y°y°

4 4 Practice: 1) 2)

5 5 Exterior Angles An angle formed by two secants, two tangents, or a secant and a tangent drawn from a point outside the circle. 3 y  x  2 y  x  1 x  y  Two secants A secant and a tangent 2 tangents

6 6 Angles Outside the Circle Theorem (Exterior Angle Theorem) The measure of the angle formed is equal to ½ the difference of the intercepted arcs.

7 7 Example: Exterior Angle Theorem

8 8 Q G F D E C 1 2 3 4 5 6 A 100° 30° 25°

9 9 Practice: 1) 2)

10 10 An Angle Formed by a Chord and a Tangent 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.

11 11 Practice: 1) 2)


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