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
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
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Inscribed Angle An angle whose vertex is on the
circle and whose sides are chords of the circle
INTERCEPTEDARC
INSCRIBEDANGLE
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Determine whether each angle is an inscribed
angle. Name the intercepted arc for the angle.
1.
5
Determine whether each angle is an inscribed
angle. Name the intercepted arc for the angle.
2.
Q
V
K
R
S
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To find the measure of an inscribed angle
1600
800
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What do we call this type of angle?
What is the value of x?
What do we call this type of angle?
How do we solve for y?
The measure of the inscribed angle is HALF the
measure of the inscribed arc!!
120
x
y
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Examples
3. If m JK 80?, find m ltJMK.
40 ?
4. If m ltMKS 56?, find m MS.
112 ?
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If two inscribed angles intercept the same arc,
then they are congruent.
72?
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Example 5 In ?J, mlt3 5x and mlt4 2x 9. Find
the value of x.
x 3
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If all the vertices of a polygon touch the edge
of the circle, the polygon is INSCRIBED and the
circle is CIRCUMSCRIBED.
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A circle can be circumscribed around a
quadrilateral if and only if its opposite angles
are supplementary.
B
A
D
C
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Example 8 Find y and z.
z
110
110 y 180
y
y 70
85
z 85 180
z 95
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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, mlt1 6x 5 and mlt2 3x 4.
Find the value of x.
6x 5 3x 4 90 180
or 6x 5 3x 4 90
H
2
K
N
1
G
x 11
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Class work
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Homework