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Angles Formed by Tangents, Chords, and Secants. Tangent: A line that intersects the circle in exactly one point. PT is a tangent P T A.

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Presentation on theme: "Angles Formed by Tangents, Chords, and Secants. Tangent: A line that intersects the circle in exactly one point. PT is a tangent P T A."— Presentation transcript:

1 Angles Formed by Tangents, Chords, and Secants

2 Tangent: A line that intersects the circle in exactly one point. PT is a tangent P T A

3 Angle Formed by Tangent and Chord: The measure of an angle formed by a tangent and a chord intersecting at the point of tangency is one-half the measure of the intercepted arc. P T A

4 Angles Formed by Two Chords In a Circle: The measure of an angle formed by two chords intersecting in a circle is one-half the sum of the measures of the arcs intercepted by the angle and by its vertical angle. A B C D E

5 1. If mAC = 30 and m  AEC = 55, find mBD. A B C D E

6 2. If mAC = 20 and mBD = 100, find m  AEC. A B C D E

7 3. If mCB = 120 and mAD = 180, find m  AED. A B C D E

8 4. If mAC = 27 and mDB = 81, find m  DEB. A B C D E

9 5. If mAC = 20 and m  AEC = 70, find mBD. A B C D E

10 6. If mBD = 75 and m  DEB = 60, find mAC. A B C D E

11 7. If mAB = 100 find m  ABC. A B C D

12 8. m  ABC = 75, find mAB. A B C D

13 9. If m  ABD = 110, find mAEB. A B C D E

14 10. If mAEB = 105, find m  ABD A B C D E


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