Lesson 9.2A R.4.G.5 Investigate and use the properties of angles (central and inscribed) arcs, chords, tangents, and secants to solve problems involving circles
Lesson 9.2A R.4.G.5 Investigate and use the properties of angles (central and inscribed) arcs, chords, tangents, and secants to solve problems involving.
Dec 29, 2015
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Lesson 9.2AR.4.G.5 Investigate and use the properties of angles (central and inscribed) arcs, chords, tangents, and
secants to solve problems involving circles
Intercepted ArcA piece of a circle contained between the two rays of an angle
Central AngleAn angle inside a circle with its vertex at the center of the circle
Inscribed AngleAn angle inside a circle with its vertex on the circle
• Arc measures always given in degrees.
• The measure of a central angle is equal to the measure of the intercepted arc.
• The measure of the inscribed angle is one half of the measure of the intercepted arc.
• A tangent line is always perpendicular to the radius or diameter drawn to the point of tangency.
Find the value of the variables:
xo
A
C
B
xo
AC
B
30O
Find the value of the variables:
150o
AB
xO
yo
AC
B60O
Given that AB is tangent to the circle, find the value of x.
37o
xo
A
BC
Given that CD is tangent to the circle, find the value of x.
xo
72oC
D
E
Given that AB and AD are both tangent to the circle, find the value of x.
140o
xoA
B
D
C
Given that PQ and PS are both tangent to the circle, find the value of x.
150o
xoP
Q
S
T
Remember, the radius of a circle never changes, regardless of what point on the circle it’s drawn to.
Find the value of x, given circle O and the following segment lengths: AC = 16, OB = 12, OE = x. If your answer is not an integer, round to the nearest tenth.
x
A CB
O
E
Find the value of x, given circle O and the following segment lengths: AC = 50, OB = 20, OE = x. If your answer is not an integer, round to the nearest tenth.
x
A CB
O
E
Find the value of x, given circle P and the following segment lengths: MN = 35, PS = 10, ST = x. If your answer is not an integer, round to the nearest tenth.
M N
S
P
T
Find the value of x, given circle P and the following segment lengths: MN = 18, PS = 5, ST = x. If your answer is not an integer, round to the nearest tenth.
M
N
S
P
T
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