1. Daily Check

2. Homework Review

3. How can I find a segment length for a piece of a chord?
GPS Geometry Day 25 ( )
UNIT QUESTION: What special properties are found with the parts of a circle?
Standard: MMC9-12.G.C.1-5,G.GMD.1-3
Today’s Question:
How can I find a segment length for a piece of a chord?
Standard: MMC9-12.G.C.2

4. How do you know when two chords are congruent?
corresponding arcs are congruent B A M P L
b. equidistant from the center C
Discuss that these are “if and only if statements”. Give some basic examples.
LP  PM
ALP = BMP = 90 D

5. 2x
x + 40

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

7. IF AC is the perpendicular bisector of segment DB, then…
It’s the DIAMETER!!!
Arcs DC and BC are congruent!!! A C
Discuss “if and only if” and two things must be true to prove the third is true: diameter, perpendicular, bisects. Give some basic examples. B

8. IN Q, KL  LZ. IF CK = 2X + 3 and
CZ = 4x, find x. Q
x = C Z K L

9. In P, if PM  AT, PT = 10, and PM = 8, find AT.
MT = T
AT =

10. Your turn! 
ÐUTV  ÐXTW.
Find WX.___________
Find ___________

11. Your turn! 
Find the length of each chord.
CE = _______
LN = _______

12. Segment Lengths in Circles
Find the lengths of segments of chords
Find the lengths of segments of tangents and secants

13. ab = cd Two chords intersect Type 1: INSIDE the circle a d c b
Emphasize that the chords are NOT congruent or bisected!

14. Solve for x. 9 6 x
x = 2

15. x = DB = Find the length of DB. 12 2x 8 3x A D C B
What can we conclude about AC? C B

16. Find the length of each chord.
x =
AC =
DB = A
x - 4 x 5 C 10 B

17. EA • EB = EC • ED Two secants intersect Type 2: OUTSIDE the circle E A

18. Ex: 3 Solve for x. B 13 A 7 E 4 C x D 7
(7 + 13) = 4
(4 + x)
x = 31
140 = x
124 = 4x

19. Ex: 4 Solve for x. B x A 5 D 8 6 C E 6
(6 + 8) = 5
(5 + x)
84 = x
x = 11.8
59 = 5x

20. Type 2 (with a twist):
Secant and Tangent C B E A
EA2 = EB • EC

21. x = 36 242 = 12 (12 + x) 576 = 144 + 12x x 12 24 Ex: 5 Solve for x. CB x 12 E 24 A
242 = 12
(12 + x)
x = 36
576 = x

22. Ex: 6 5 B E 15 C x A x2 = 5
(5 + 15)
x2 = 100
x = 10

23. Homework
Practice Worksheet