Warm up
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Warm up3080100180
100260
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Wheel of Formulas!!
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Central Angle
Angle = Arc
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Inscribed Angle
• Angle where the vertex is ON the circle
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Inscribed Angle
ARCANGLE =
2
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2
ArcdIntercepteAngleInscribed
160
80
The arc is twice as big as the angle!!
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120
x
y
Find the value of x and y.
120
60
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Examples1. If mJK = 80 and JMK = 2x – 4, find x.
M
Q
K
S
J
2. If mMKS = 56, find m MS.
x = 22
112
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72˚
If two inscribed angles intercept the same arc, then they are congruent.
Find the measure of DOG and DIG D
O
G
I
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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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Quadrilateral inscribed in a circle: opposite angles are SUPPLEMENTARY
A B
CD
180 CmAm180 DmBm
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If a right triangle is inscribed in a circle then the hypotenuse is the diameter of the circle.
diameter
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Example 3
In J, m3 = 5x and m 4 = 2x + 9.Find the value of x.
3
Q
D
JT
U
4
x = 3
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4x – 14 = 90
H
K
GN
Example 4
In K, GH is a diameter and mGNH = 4x – 14. Find the value of x.
x = 26
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z
y
110
85
110 + y =180y = 70
z + 85 = 180z = 95
Example 5 Find y and z.