1. 2. Find m1 1. Find mXAB 42º 90º 3. Find mZ 70º Session 71 WARM UP A
222º D C
90º
3. Find mZ
55º Z
Think!!
70º

2. Two chords intersect
INSIDE the circle
Type 1: a
ab = cd d c b

3. Example 1: 9 12 6 3 x x 2 2
X = 3
X = 8 x 3 6 2
X = 1

4. Example 2: Find x
2x  3x = 12  8 8 12 2x 3x
6x2 = 96
x2 = 16
x = 4

5. EA * EB = EC * ED Two secents intersect Type 2: OUTSIDE the circle E A

6. 7 (7 + 13) = 4 (4 + x) x = 31 140 = 16 + 4x 124 = 4x Example 3: B 13 AC x D 7
(7 + 13) = 4
(4 + x)
x = 31
140 = x
124 = 4x

7. 5 (5 + x) = 6 (6 + 8) x = 11.8 25+5x = 84 59 = 5x Example 4: B x A 5 DC 6 E 5
(5 + x) = 6
(6 + 8)
x = 11.8
25+5x = 84
59 = 5x

8. Notice that on the tangent segment, the outside is the whole!
Secant Segment
External
Segment
Tangent Segment

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

10. Example 5: C B x 12 E 24 A
242 = 12
(12 + x)
576 = x
x = 36

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

12. What you should know by now…
Given two chords
Given two secants OR a tangent and a secant