Circles Lines and Angles
Circles Lines and Angles
Circles Lines and Angles
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Geometry<br />
HS Mathematics<br />
Unit: 07 Lesson: 01<br />
<strong>Circles</strong>, <strong>Lines</strong>, <strong>and</strong> <strong>Angles</strong><br />
Special Segments<br />
1. Tangent – a line, ray or line segment that intersects a circle in exactly one point called the<br />
point of tangency. A tangent contains no interior points of the circle <strong>and</strong> is perpendicular to the<br />
radius at the point of tangency.<br />
X<br />
Y<br />
T<br />
S<br />
2. Secant – a line, ray, or line segment that intersects the circle in exactly two points. A secant<br />
contains a chord of the circle.<br />
L<br />
M<br />
P<br />
N<br />
3. <strong>Angles</strong> Formed by Special Segments<br />
The measure of a central angle is equal<br />
to the intercepted arc.<br />
Q<br />
R<br />
P<br />
mQPR<br />
mQR<br />
The measure of an inscribed angle is<br />
one-half the intercepted arc.<br />
L<br />
M<br />
N 1<br />
mLMN<br />
mLN<br />
2<br />
©2012, TESCCC 09/26/12 page 1 of 4
Geometry<br />
HS Mathematics<br />
Unit: 07 Lesson: 01<br />
<strong>Circles</strong>, <strong>Lines</strong>, <strong>and</strong> <strong>Angles</strong><br />
If two secants intersect in the interior of a circle, then the measure of an angle formed is one-half<br />
the sum of the measures of the arcs intercepted by the angles.<br />
1 = ______ 2 = ______<br />
3 = ______ 4 = ______<br />
60 o<br />
2<br />
1<br />
4<br />
3<br />
50 o<br />
If the segments (two secants, a secant <strong>and</strong> a tangent, or two tangents) intersect in the exterior of<br />
a circle, the measure of the angle formed is one-half the positive difference of the measures of the<br />
intercepted arcs.<br />
1<br />
30 o 110o<br />
160 o<br />
70 o<br />
1<br />
1 = ______ 1 = ______<br />
242 o<br />
1<br />
1 = ______<br />
©2012, TESCCC 09/26/12 page 2 of 4
Geometry<br />
HS Mathematics<br />
Unit: 07 Lesson: 01<br />
<strong>Circles</strong>, <strong>Lines</strong>, <strong>and</strong> <strong>Angles</strong><br />
Guided Practice<br />
1. Given Circle P<br />
S<br />
mSPT = 120 o<br />
mTQR= 25 o<br />
P T<br />
Q<br />
O<br />
R<br />
mTR 30 o<br />
Find<br />
a. mOR b. mOS<br />
c. mST d. mSOR<br />
2. Given Circle M<br />
J<br />
F<br />
G<br />
E<br />
H<br />
K<br />
M<br />
I<br />
mGK 50 o<br />
mKI 4x<br />
40<br />
mIE<br />
x <br />
45<br />
mEF x 25<br />
mFG x<br />
Find<br />
a. m<br />
J<br />
b. m<br />
KIJ<br />
c. m JKI<br />
d. m<br />
IHE<br />
e. m GIF<br />
f. m<br />
FHE<br />
©2012, TESCCC 09/26/12 page 3 of 4
Geometry<br />
HS Mathematics<br />
Unit: 07 Lesson: 01<br />
<strong>Circles</strong>, <strong>Lines</strong>, <strong>and</strong> <strong>Angles</strong><br />
Practice Problems<br />
Find the indicated measures for Circle E.<br />
ADC<br />
<br />
60 o<br />
B<br />
AD DC<br />
mBF 6<br />
A<br />
F<br />
C<br />
E<br />
D<br />
1. AC 2. ABC<br />
3. FBC<br />
4. BC<br />
5. AEC<br />
6. BEC<br />
7. CD 8. EAD<br />
©2012, TESCCC 09/26/12 page 4 of 4
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