1. Over Lesson 10–4 A.A B.B C.C D.D 5-Minute Check 1 60 Refer to the figure. Find m  1.

2. Over Lesson 10–4 A.A B.B C.C D.D 5-Minute Check 2 20 Refer to the figure. Find m  2.

3. Over Lesson 10–4 A.A B.B C.C D.D 5-Minute Check 4 100 Refer to the figure. Find m  4.

4. Over Lesson 10–4 A.A B.B C.C D.D 5-Minute Check 5 11 find x if m  A = 3x + 9 and m  B = 8x – 4.

5. Then/Now Use properties of tangents. Solve problems involving circumscribed polygons. In this lesson we will:

6. Vocabulary tangent point of tangency common tangent

7. Example 1 Identify Common Tangents A. Copy the figure and draw the common tangents. If no common tangent exists, state no common tangent. Answer: These circles have no common tangents. Any tangent of the inner circle will intercept the outer circle in two points.

8. Example 1 Identify Common Tangents B. Copy the figure and draw the common tangents. If no common tangent exists, state no common tangent. Answer: These circles have 2 common tangents.

9. A.A B.B C.C D.D Example 1 4 common tangents A. Copy the figure and draw the common tangents to determine how many there are. If no common tangent exists, choose no common tangent.

10. A.A B.B C.C D.D Example 1 3 common tangents B. Copy the figure and draw the common tangents to determine how many there are. If no common tangent exists, choose no common tangent.

11. Concept

12. Example 2 Identify a Tangent Test to see if ΔKLM is a right triangle. ? 20 2 + 21 2 = 29 2 Pythagorean Theorem 841 =841  Simplify. Answer:

13. A.A B.B Example 2 A. B.

14. Example 3 Use a Tangent to Find Missing Values EW 2 + DW 2 =DE 2 Pythagorean Theorem 24 2 + x 2 =(x + 16) 2 EW = 24, DW = x, and DE = x + 16 576 + x 2 =x 2 + 32x + 256Multiply. 320 =32xSimplify. 10 =xDivide each side by 32. Answer: x = 10

15. A.A B.B C.C D.D Example 3 12

16. Concept

17. Example 4 Use Congruent Tangents to Find Measures AC =BCTangents from the same exterior point are congruent. 3x + 2 =4x – 3Substitution 2 =x – 3Subtract 3x from each side. 5 =xAdd 3 to each side. Answer: x = 5

18. A.A B.B C.C D.D Example 4 7

19. Example 5 Find Measures in Circumscribed Polygons Step 1Find the missing measures.

20. Example 5 Find Measures in Circumscribed Polygons Step 2Find the perimeter of ΔQRS. Answer: So, the perimeter of ΔQRS is 36 cm. = 10 + 2 + 8 + 6 + 10 or 36 cm

21. A.A B.B C.C D.D Example 5 56 cm