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Wheel of Formulas!!

Central Angle

Angle = Arc

Inscribed Angle

• Angle where the vertex is ON the circle

Inscribed Angle

ARCANGLE =

2

2

ArcdIntercepteAngleInscribed

160

80

The arc is twice as big as the angle!!

120

x

y

Find the value of x and y.

120

60

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

72˚

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

Find the measure of DOG and DIG D

O

G

I

If all the vertices of a polygon touch the edge of the circle, the polygon is INSCRIBED and the circle is CIRCUMSCRIBED.

Quadrilateral inscribed in a circle: opposite angles are SUPPLEMENTARY

A B

CD

180 CmAm180 DmBm

If a right triangle is inscribed in a circle then the hypotenuse is the diameter of the circle.

diameter

Example 3

In J, m3 = 5x and m 4 = 2x + 9.Find the value of x.

3

Q

D

JT

U

4

x = 3

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

z

y

110

85

110 + y =180y = 70

z + 85 = 180z = 95

Example 5 Find y and z.