Warm up
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Warm up. 30 . 8 0 . 100 . 180 . 100 . 260 . Wheel of Formulas!!. Central Angle. Angle = Arc. Inscribed Angle. Angle where the vertex is ON the circle. Inscribed Angle. 160 . The arc is twice as big as the angle!!. 80 . Find the value of x and y. 120 . . 120 . x.

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Warm up

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Warm up

Warm up

30

80

100

180

100

260


Wheel of formulas

Wheel of Formulas!!


Central angle

Central Angle

Angle = Arc


Inscribed angle

Inscribed Angle

  • Angle where the vertex is ON the circle


Inscribed angle1

Inscribed Angle


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160

The arc is twice as big as the angle!!

80


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Find the value of x and y.

120

120

x

60

y


Examples

J

K

Q

S

M

Examples

1. If mJK= 80 and JMK = 2x – 4, find x.

x = 22

2. If mMKS= 56, find m MS.

112


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Find the measure of DOG and DIG

D

72˚

G

If two inscribed angles intercept the same arc, then they are congruent.

O

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

B

A

D

C


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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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Q

D

3

J

T

4

U

Example 3

In J, m3 = 5x and m 4 = 2x + 9.

Find the value of x.

x = 3


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Example 4

In K, GH is a diameter and mGNH = 4x – 14. Find the value of x.

4x – 14 = 90

H

K

x = 26

N

G


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Example 5 Find y and z.

z

110

110 + y =180

y

y = 70

85

z + 85 = 180

z = 95


Practice ws

Practice WS

10 problems


Homework ws

Homework WS

6.4 Practice


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