1. 1) What is the Triangle Exterior Angle Theorem?
2) Solve for x. 3) Solve for y.
(5x)° R Q T S A B C D
(2y - 3)°
(y - 1)°

2. Secant is a line that intersects a circle at two points.B A
Secant is a line that intersects
a circle at two points. F E

3. Theorem
If two secants or chords intersect in the interior of a circle, then the measure of each angle formed is half the sum of the measures of its intercepted arcs. A B C D 1 E
Chords AD and BC intersect at E.
m<1 = ½ (mAB +mCD)

4. Find each angle measure. 1. Find m<SQR
Examples
Find each angle measure. 1. Find m<SQR
2. Find m<ABE A B C D E
65°
37° P S Q T R
100°
32°
3. Find mMQ M R Q P N
160°
255°

5. You try Find m<AEB 5. Find mRS 6. Find m<LPO R S N L T 90° 100°C
139°
113° L O P M N
65°
6. Find m<LPO
80°

6. Theorem If a tangent and a secant, two tangents, or two secants intersect in the exterior of a circle, then the measure of the angle formed is half the difference of the measures of its intercepted arcs.
Two Tangents
Tangent and Secant
Two Secants E F G H 2 C B D A 1 L K M N J 3
m<1 = ½ (mAD – mBD)
m<2 = ½ (mEHG – mEG)
m<3 = ½ (mJN – mKM)

7. Examples 1. 2. 3. E F G x° 132° P Q S R x° 174° 98° L K M N J x° 83°
25° 3.

8. P Q S R x°
200°
74° 4. E F G x°
225° 5. L K M N J x°
30°
25° 6.

9. Summing Up Angles in Circles
Where’s the Vertex?
What’s the Angle Measure?
Examples 2
200°
m<2=100°
Vertex on a circle 1
120°
m<1=60°
Half of the arc
Vertex inside
a circle
Half of the arcs added
44° 1
m<1= ½ (44°+86°)
= 65°
86° 1
78°
202° 2
45°
125°
Vertex outside
a circle
Half of the arcs subtracted
m<2= ½ (125°-45°)
= 40°
m<1= ½ (202°-78°)
= 62°

10. Whiteboards
Practice 12-4 Workbook
P 491 #1-12 all

11. Warm Up 1. Find mAF 2. Find LP 3. Find mYZ mLR= 100° L M N S R P Q 80°
26°
mLR= 100° A D E F B C
160°
110°
48°
On the white boards!
3. Find mYZ
68°
113°
49° X Y Z W

12. Last 4 m<FGJ m<HJK Solve for x 4. mCE E F G 31° 52° H J 130° K D
150° A B C D E G H J
25°
48°
83°
Common mistakes:
#1) Said 52, assumed that G was center
Said 10.5, subtracted arcs instead of adding them
#2) Said 90 instead of 65, assuming that HJ was diameter
Said 130 instead of 65, assuming central angle

13. P 681 # 5 – 24 all, 36
P 691 # 2-14 even, even
Period 1 Due Tuesday
Period 2/4 Due Wednesday
Exam on Thurs/Fri