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5-Minute Check on Lesson 10-4

Transparency 10-5. 5-Minute Check on Lesson 10-4. Refer to the figure and find each measure . m 1 m2 m3 m4 In ⊙ B, find x if m A = 3x + 9 and mB = 8x – 4.

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5-Minute Check on Lesson 10-4

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  1. Transparency 10-5 5-Minute Check on Lesson 10-4 • Refer to the figure and find each measure. • m1 • m2 • m3 • m4 • In ⊙B, find x if mA = 3x + 9and mB = 8x – 4. • If an inscribed angle has a measure of 110, what is the measure of its intercepted arc? 60° 20° 20° 100° x = 11 Standardized Test Practice: 55 70 110 220 A B C D D Click the mouse button or press the Space Bar to display the answers.

  2. Lesson 10-5 Tangents

  3. Objectives • Use properties of tangents • Solve problems involving circumscribed polygons

  4. Vocabulary • Tangent – a line that intersects a circle in exactly one point • Point of tangency – point where a tangent intersects a circle

  5. ALGEBRA is tangent to at point R. Find y. Because the radius is perpendicular to the tangent at the point of tangency, . This makes a right angle and  a right triangle. Use the Pythagorean Theorem to find QR, which is one-half the length y. Example 5-1a

  6. Answer: Thus, y is twice . Example 5-1b Pythagorean Theorem Simplify. Subtract 256 from each side. Take the square root of each side. Because y is the length of the diameter, ignore the negative result.

  7. is a tangent to at point D. Find a. Example 5-1c Answer: 15

  8. Determine whether is tangent to Answer: So, is not tangent to . Example 5-2a First determine whether ABCis a right triangle by using the converse of the Pythagorean Theorem. Pythagorean Theorem Because the converse of the Pythagorean Theorem did not prove true in this case, ABC is not a right triangle.

  9. Determine whether is tangent to Answer: Thus, making a tangent to Example 5-2c First determine whether EWDis a right triangle by using the converse of the Pythagorean Theorem. Pythagorean Theorem Simplify. Because the converse of the Pythagorean Theorem is true, EWD is a right triangle and EWD is a right angle.

  10. Determine whether is tangent to Example 5-2f Answer: no

  11. are drawn from the same exterior point and are tangent to so are drawn from the same exterior point and are tangent to Example 5-3a ALGEBRA Find x. Assume that segments that appear tangent to circles are tangent.

  12. Example 5-3b Definition of congruent segments Substitution. Use the value of y to find x. Definition of congruent segments Substitution Simplify. Subtract 14 from each side. Answer: 1

  13. Triangle HJK is circumscribed about Find the perimeter of HJK if We are given that Example 5-4a Use Theorem 10.10 to determine the equal measures. Definition of perimeter Substitution Answer: The perimeter of HJKis 158 units.

  14. Triangle NOT is circumscribed about Find the perimeter of NOT if Example 5-4c Answer: 172 units

  15. Summary & Homework • Summary: • A line that is tangent to a circle intersects the circle in exactly one point. • A tangent is perpendicular to a radius of a circle • Two segments tangent to a circle form the same exterior point are congruent • Homework: • pg 556-558; 8-11, 12-17

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