for each circle c, find the value of x. assume that segments that appear to be tangent are tangent....
TRANSCRIPT
C
x4
8
A
B
C
D
7x - 2
3x + 8
For each circle C, find the value of x. Assume that segments that appear to be tangent are tangent.
1) 2)
Math II
UNIT QUESTION: What special properties are found with the parts of a circle?Standard: MM2G1, MM2G2
Today’s Question:What is the relationship of an inscribed angle to the measure of its intercepted arc?Standard: MM2G3.b
Inscribed Angle: An angle whose
vertex is on the circle and
whose sides are chords of the circle
INSCRIBEDANGLE
INTER
CEP
TED
ARC
Determine whether each angle is an inscribed angle. Name the intercepted arc for the angle.
C
L
O
T1.
YES; CL
Determine whether each angle is an inscribed angle. Name the intercepted arc for the angle.
Q
R
K
V2. NO;
QVR
S
2
ArcdIntercepteAngleInscribed
1600
800
To find the measure of an inscribed angle…
120
x
What do we call this type of angle?What is the value of x?
y
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!!
Examples
3. If m JK = 80, find m <JMK.
M
Q
K
S
J
4. If m <MKS = 56, find m MS.
40
112
72
If two inscribed angles intercept the same arc, then they are congruent.
Example 5
In J, m<3 = 5x and m<4 = 2x + 9.Find the value of x.
3
Q
D
JT
U
4
x = 3
If all the vertices of a polygon touch the edge of the circle, the polygon is INSCRIBED and the circle is CIRCUMSCRIBED.
A circle can be circumscribed around a quadrilateral if and only if its
opposite angles are supplementary.
A B
CD
180 CmAm180 DmBm
z
y
110
85
110 + y =180y = 70
z + 85 = 180z = 95
Example 8 Find y and z.
180
diameter
If a right triangle is inscribed in a circle then the hypotenuse is the diameter of the circle.
H
K
GN
4x – 14 = 90
Example 6
In K, m<GNH = 4x – 14. Find the value of x.
x = 26
H
K
GN
or
6x – 5 + 3x – 4 = 90
Example 7
In K, m<1 = 6x – 5 and m<2 = 3x – 4. Find the value of x.
x = 11
1
2
6x – 5 + 3x – 4 + 90 = 180
