Tuesday, November 5th

WARM UPFind

1. mKLM

2. mMNJ

Vocab Review

Fill in the Blank• A secant line cross the circle

_________times. • Tangent line touches the circle

_________. • A chord has both __________ on the

circle• The diameter is ________the length

of the radius

CentralAngles

HWANSWERS

Inscribed Angles

P

A

B

Central ANGLE = ARC

Case I: Central Angle: Vertex isAT the center

Case II: Inscribed Angle: Vertex is ON circle

ANGLE = ARC

2ANGLE

ARCANGLE

ARC

This means division!!

2

ArcdIntercepteAngleInscribed

160

80

The arc is twice as big as the angle!!

120

x

y

Find the value of x and y

Examples1. If mJK = 80 and <JMK = 2x – 4, find x.

M

Q

K

S

J

2. If m<MKS = 56, find m MS.

x = 22

112

If all the vertices of a polygon touch the edge of the circle, the polygon is

INSCRIBED and the circle is CIRCUMSCRIBED.

72˚

If two inscribed

angles intercept the

same arc, then they are

congruent.

Find the measure of DOG and DIG D

O

G

I

Example 3

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

3

Q

D

JT

U

4

x = 3

If a right triangle is inscribed in a circle then the

hypotenuse is the diameter of the circle.

diameter

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

Bonus: What type of triangle is this? Why?

Classwork

Work together on

1-8

Homework

Pick Evens or Odds