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10.6 Secants, Tangents, & Angle Measures

10.6 Secants, Tangents, & Angle Measures. Objectives. Find measures of angles formed by lines intersecting on, inside, or outside a circle. A. D. O. C. B. Secants and Interior Angles.

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10.6 Secants, Tangents, & Angle Measures

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  1. 10.6 Secants, Tangents, & Angle Measures

  2. Objectives • Find measures of angles formed by lines intersecting on, inside, or outside a circle.

  3. A D O C B Secants and Interior Angles Theorem 10.12:If two secants intersect in the interior of a , then the measure of an  formed is ½ the measure of the sum of the arcs intercepted by the secants that created the . mAOC = ½ (m arc AC + m arc DB) mAOD = ½ (m arc AD + m arc CB)

  4. Find if and Example 1: Method 1

  5. Example 1: Method 2 Answer: 98

  6. Find if and Your Turn: Answer: 138

  7. D A O C B F Secants, Tangents and Angles Theorem 10.13:If a secant and a tangent intersect at the point of tangency, then the measure of each  formed is ½ the measure of its intercepted arc. mDOB = ½ (m arc OB) mCOB = ½ (m arc OFB)

  8. Find if and Example 2: Answer: 55

  9. Find if and Your Turn: Answer: 58

  10. A G B F H O I C E D Secants – Tangents & Exterior Angles Theorem 10.14:If two secants, a secant and a tangent, or two tangents intersect in the exterior of a circle, then the measure of the  formed is ½ the measures of the difference of the intercepted arcs. mBOC = ½ (m arc BC – m arc HI) mAOC= ½ (m arc AC – m arc AI)mAED= ½ (m arc ABD – m arc AD)

  11. Example 3: Find x. Theorem 10.14 Multiply each side by 2. Add x to each side. Subtract 124 from each side. Answer: 17

  12. Your Turn: Find x. Answer: 111

  13. Example 4: A jeweler wants to craft a pendant with the shape shown. Use the figure to determine the measure of the arc at the bottom of the pendant. Let x represent the measure of the arc at the bottom of the pendant. Then the arc at the top of the circle will be 360 – x. The measure of the angle marked 40° is equal to one-half the difference of the measure of the two intercepted arcs.

  14. Example 4: Multiply each side by 2 and simplify. Add 360 to each side. Divide each side by 2. Answer: 220

  15. Two sides of a fence to be built around a circular garden in a park are shown. Use the figure to determine the measure of Your Turn: Answer: 75

  16. Example 5: Find x. Multiply each side by 2. Add 40 to each side. Divide each side by 6. Answer: 25

  17. Your Turn: Find x. Answer: 9

  18. Assignment • Pre-AP GeometryPg. 564 #12 - 32 • Geometry:Pg. 564 #3 – 7, 12 - 26

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