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Chapter 10 : Circles

10.5.1 Apply Other Angle Relationships in Circles. Chapter 10 : Circles. If a chord intersects a tangent then the measure of the angle is one half the measure of the intercepted arc. Chord Tangent Intersect Theorem. m1= ½ mACB. C. A. m2= ½ mAB. 1. 2. B.

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Chapter 10 : Circles

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  1. 10.5.1 Apply Other Angle Relationships in Circles Chapter 10: Circles

  2. If a chord intersects a tangent then the measure of the angle is one half the measure of the intercepted arc Chord Tangent Intersect Theorem m1= ½ mACB C A m2= ½ mAB 1 2 B

  3. The measure of each angle is one half the sum of the intercepted arcs Angles Inside a Circle Theorem Since 1  2 m1 = m2 = ½ (mCD + m AB) A m3 = m4 = ½ (mCA + mBD) 4 2 C B 1 3 D

  4. If an angle is outside the circle the measure of the circle is one half the difference of the intercepted arc • 3 cases, same rule: Angles Outside a Circle Theorem A B 1 C A A 1 B C C 1 B D m1 = ½ (mABC – mCA) m1 = ½ (mAB – mCD) m1 = ½ (mAC – mCB)

  5. Find the value of each arc D 60⁰ A B 40⁰ F 80⁰ C E

  6. p. 683 1 – 6, 10 – 13, 16 - 20, 23 – 27odd, 32 -38even Homework

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