1. 10.5 Apply Other Angle Relationships in Circles
Hubarth
Geometry

2. Theorem 10.11
If a tangent and a chord intersect at a point on a circle, then the
measure of each angle formed is one half the measure of its
intercepted arc. . B C 2 1 A

3. Ex 1 Find Angle and Arc Measures
Line m is tangent to the circle. Find the measure of the red angle or arc. = 12
(130o) b.
m KJL a. m
= 65o = 2
(125o)
= 250o

4. . Theorem 10.12 Angles Inside the Circle Theorem
If two chords intersect inside a circle, then the measure
of each angle is one half the sum of the measure of the
arcs intercepted by the angle and its vertical angle. D A 1 2 B C
Theorem Angles Outside the Circle Theorem
If a tangent and a secant, two tangents or two secants intersect outside a circle, then the
measure of the angle formed is one half the difference of the measures of the intercepted
arcs. P X B . A Q W 1 2 3 Z Y C R

5. Ex 2 Find an Angle Measure Inside a Circle
Find the value of x. xo = 12
(mJM + mLK) xo = 12
(130o + 156o) xo
= 143

6. Ex 3 Find and Angle Measure Outside a Circle
Find the value of x.
The tangent CD and the secant CB intersect outside the circle.
m BCD
(mAD – mBD) = 12 = 12
(178o – 76o) xo
= 51 x

7. Find the indicated measure.
Practice
Find the indicated measure. = 12
(210o)
m RST m
= 105o = 2
(98o)
= 196o
m XY = 2
(80o)
= 160o
Find the value of the variable. 5. 6.
= 104o a xo
253.7o
y = 61o