Warm up3080100180

100260

Inscribed Angles and Inscribed

Quadrilaterals

Central Angle

Central Angle = Arc

Inscribed Angle• Angle where the vertex is ON the circle

Inscribed Angle

Inscribed Angle = intercepted Arc/2

160

80

The arc is twice as big as the angle!!

ARCANGLE =

2

Inscribed angles

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

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

congruent.

BAD =BCD

A

B

C

D

Find the measure of DOG ,DIG, ODI and OGI

D

O

G

I

102

74

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

5x = 2x + 9

x = 3

3x = + 9

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

4x = 104

z

2x + 18

85

2x +18 + 22x – 6 = 180

x = 7

z + 85 = 180z = 95

Example 5 Solve for x and z.

22x – 6 24x +12 = 18024x = 168

Textbook

p. 420#2 – 13 (omit

#6), 17 – 20, 22