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5-Minute Check on Lesson 10-5

Transparency 10-6. 5-Minute Check on Lesson 10-5. Determine whether each segment is tangent to the given circle . BC 2. QR Find x. Assume that the segments that appear to be tangents are tangents.

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5-Minute Check on Lesson 10-5

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  1. Transparency 10-6 5-Minute Check on Lesson 10-5 • Determine whether each segment is tangent to the given circle. • BC 2. QR • Find x. Assume that the segments that appear to be tangents are tangents. • 3. 4. • 5. What is the measure of PS? Yes No x = 20√5 or 44.72 x = 12 Standardized Test Practice: A B C D 18 10 B 12 14 Click the mouse button or press the Space Bar to display the answers.

  2. Lesson 10-6 Secants, Tangents, and Angle Measures

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

  4. Vocabulary • Secant – a line that intersects a circle in exactly two points

  5. y x Circles – Secants Interior Angles formed by a Secant & a Tangentm3 = ½ (m Arc JMK) m4 = ½ (m Arc JLK) M 3 K 2 4 1 J P Center Interior Angles formed by 2 Secantsm1 = ½ (m Arc MJ + m Arc LK) m2 = ½ (m Arc MK + m Arc JL) L

  6. Circles – External Angles Two Secants Secant & Tangent Two Tangents J J J K K L S T T M M M N mJ = ½(m Arc TM – m Arc TK) mJ = ½|m Arc TM – m Arc TK| mJ = ½(m Arc TMS – m Arc TS) mJ = ½|m Arc TMS – m Arc TS| mJ = ½(m Arc MN – m Arc LK) mJ = ½|m Arc MN – m Arc LK|

  7. Find if and Example 6-1a Method 1

  8. Example 6-1b Method 2 Answer: 98

  9. Find if and Example 6-1d Answer: 138

  10. Find if and Example 6-2a Answer: 55

  11. Find if and Example 6-2c Answer: 58

  12. Example 6-3a Find x. Theorem 10.14 Multiply each side by 2. Add x to each side. Subtract 124 from each side. Answer: 17

  13. Example 6-3c Find x. Answer: 111

  14. Example 6-4a JEWELRY 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 1/2 the difference of the measure of the two intercepted arcs. Multiply each side by 2 and simplify. Add 360 to each side. Divide each side by 2. Answer: 220

  15. PARKS 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 Example 6-4c Answer: 75

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

  17. Example 6-5c Find x. Answer: 9

  18. Summary & Homework • Summary: • The measure of an angle formed by two secant lines is half the positive difference of its intercepted arcs • The measure of angle formed by a secant and tangent line is half its intercepted arc • Homework: • pg 564-566; 12-14, 18-20; 23-24, 26, 29, 34-36

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