1. Challenge of the Day Find the Area

2. Chord Properties and Segments Lengths in Circles

3. If two chords are congruent, then their corresponding arcs are congruent.

4. 1.Solve for x.
8x – 7
3x + 3
8x – 7 = 3x + 3
x = 2

5. 2.Find the length of WX.

6. 3. Find
360 – 100
260 divided by 2
130º

7. If two chords are congruent, then they are equidistant from the center.

8. 4. In K, K is the midpoint of RE
4. In K, K is the midpoint of RE. If TY = -3x + 56 and US = 4x, find the length of TY. U T K E
x = 8 R S Y
TY = 32

9. If a diameter is perpendicular to a chord, then it also bisects the chord. This results in congruent arcs too. Sometimes, this creates a right triangle & you’ll use Pythagorean Theorem.

10. x = 1.5 5. IN Q, KL  LZ. If CK = 2x + 3 and CZ = 4x, find x. Q C Z K

11. MT = 6 AT = 12 6. In P, if PM  AT, PT = 10, and PM = 8, find AT. P A

12. 30 7. Find the length of CE x BD is a radius. CB is a radius.
What is the length of the radius? 25
Now double it to find CE. 30 25 x

13. LN = 96 8.Find the length of LN. MK and KL are radii.
Now double it to find LN. x 50
LN = 96

14. Segment Lengths in Circles

16. Go down the chord and multiply
Two chords intersect
INSIDE the circle
Type 1:
part
part
part
part
Emphasize that the chords are NOT congruent or bisected!
Go down the chord and multiply

17. 9. Solve for x. 9 6 x 2
x = 3

18. 10. Find the length of DB. 8 12 2x 3x A D
x = 4 C
DB = 20 B

19. 11. Find the length of AC and DB.
x – 4 x 5 C 10
x = 8
AC = 13
DB = 14 B

20. Practice
Segment Practice (1) 1-8

21. Intersections of Circles and Tangent Segments

22. S
If two segments from the same exterior point are tangent to a circle, then they are congruent. R T
Party hat problems!

23. 1. Find the value of x. R S T

24. 2. Find the value of x. R S T

25. 3. Find the value of x. C A B

26. 4. Find the value of x. B 3 A C 4 P D E

27. 5. Find the length of NP. N 8 8 T S 10 4 P R Q

28. x = 15 92 + 122 = x2 leg2 + leg2 = hyp2 6. Find the value of x. A 12 B

29. RQ = 16 122 + (RQ)2 = 202 leg2 + leg2 = hyp2 7. Find the length of RQ.8 R Q
RQ = 16

30. 8. Is CB tangent to the circle?
leg2 + leg2 = hyp2? A 32
= 322 ? C 16 24 B No

31. r = 10 320 = 32r r2 + 242 = (r + 16)2 9. Find the radius.C
r = 10 24 B

32. 10. A green on a golf course is in the shape of a circle
10. A green on a golf course is in the shape of a circle. Your golf ball is 8 feet from the edge of the green and 32 feet from a point of tangency on the green.
What is the radius?
b) How far is your ball from the cup at the center?
x = 60 ft.
x = 68 ft.

33. Two circles can intersect:
in two points
one point
or no points

34. TWO points of intersection

35. One point of intersection are called Tangent Circles
Externally Tangent
Internally Tangent

36. Have no points of intersection, but the same center
Concentric Circles
Have no points of intersection, but the same center
Same center but different radii

37. No points of intersection, but different centers

38. 5.4 – Surface Area & Volume of a Sphere

39. Segment Practice (2) all Pg. 21 – 22 (evens)
Homework
Segment Practice (2) all
Pg. 21 – 22 (evens)