1. EXAMPLE 1
Find angle and arc measures
Line m is tangent to the circle. Find the measure of the red angle or arc.
SOLUTION = 12
(130o) a.
m 1
= 65o b.
m KJL = 2
(125o)
= 250o

2. GUIDED PRACTICE
for Example 1
Find the indicated measure.
SOLUTION
m RST = 2
(98o)
= 196o

3. Find an angle measure inside a circle
EXAMPLE 2
Find an angle measure inside a circle
Find the value of x.
SOLUTION
The chords JL and KM intersect inside the circle. xo = 12
(mJM + mLK)
Use Theorem xo = 12
(130o + 156o)
Substitute. xo
= 143
Simplify.

4. Find an angle measure outside a circle
EXAMPLE 3
Find an angle measure outside a circle
Find the value of x.
SOLUTION
The tangent CD and the secant CB intersect outside the circle.
m BCD
(mAD – mBD) = 12
Use Theorem = 12
(178o – 76o) xo
Substitute.
= 51 x
Simplify.

5. GUIDED PRACTICE
for Examples 2, 3, and 4
4. Find the value of the variable.
y = 61o
ANSWER

6. GUIDED PRACTICE
for Examples 2, 3, and 4 5.
Find the value of the variable.
= 104o a
ANSWER

7. Daily Homework Quiz
Line t is tangent to the circle. Find the value of x and y. 4.
ANSWER
x = 81; y = 40.5