Daily Check

1
Daily Check
For each circle C, find the value of x. Assume
that segments that appear to be tangent are
tangent. 1) 2)
2
Questions over hw?

• 9) 42 10) 74
• 11) 286 12) 116
• 13) 318 14) 138
• 15) 222 16) 244
• 17) 138 18) 180
• 19) 7v2 20) 10v2
• 21) 135 22) 240
• 23) 225
• 1) 122 2) 90
• 3) 22 4) 115
• 5) 80 6) 180
• 7) 1 8) 10
• 9) 4 10) 9

3
Math II
UNIT QUESTION What special properties are found
with the parts of a circle? Standard MM2G1,
MM2G2 Todays Question What is the relationship
of an inscribed angle to the measure of its
intercepted arc? Standard MM2G3.b
4
________ _____
5
Inscribed Angle An angle whose vertex is on the
circle and whose sides are chords of the circle
INTERCEPTEDARC
INSCRIBEDANGLE
6
Determine whether each angle is an inscribed
angle. Name the intercepted arc for the angle.
1.
7
Determine whether each angle is an inscribed
angle. Name the intercepted arc for the angle.
2.
Q
V
K
R
S
8
To find the measure of an inscribed angle
160?
80?
9
What do we call this type of angle?
What is the value of x?
The measure of the inscribed angle is HALF the
measure of the inscribed arc!!
120
x
y
10
Examples
3. If m JK 80?, find m ?JMK.
40 ?
4. If m ?MKS 56?, find m MS.
112 ?
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If two inscribed angles intercept the same arc,
then they are congruent.
72?
12
Example 5 In ?J, m?3 5x and m? 4 2x 9. Find
the value of x.
x 3
13
If all the vertices of a polygon touch the edge
of the circle, the polygon is INSCRIBED and the
circle is CIRCUMSCRIBED.
14
A circle can be circumscribed around a
quadrilateral if and only if its opposite angles
are supplementary.
B
A
D
C
15
Example 8 Find y and z.
z
110
110 y 180
y
y 70
85
z 85 180
z 95
16
If a right triangle is inscribed in a circle then
the hypotenuse is the diameter of the circle.
180?
diameter
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4x 14 90
H
K
x 26
N
G
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Example 7 In ?K, m?1 6x 5 and m?2 3x 4.
Find the value of x.
6x 5 3x 4 90
H
2
K
x 11
N
1
G
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Classwork 6.3 and 6.4 WS
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Homework Page 207 1-18