Warm up April 22

EOCT Week 14 #2

Review HW

P

A

B

Central ANGLE = ARC

Case I: Central Angle: Vertex is AT the center

Case II: Inscribed Angle: Vertex is ON circle

ANGLE = ARC

2ANGLE

ARCANGLE

ARC

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 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.

a 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 3In J, m3 = 5x and m 4 = 2x + 9.Find the value of x.

3

QD

JT

U

4x = 3

4x – 14 = 90

HK

GN

Example 4In K, GH is a diameter and mGNH = 4x – 14. Find the value of x.

x = 26

Bonus: What type of triangle is this? Why?

z

y

110

85

110 + y =180y = 70

z + 85 = 180z = 95

Example 5 Find y and z.

Inscribed Quadrilaterals

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

INSCRIBED and the circle is CIRCUMSCRIBED.

Vocab• inscribed quadrilateral a

quadrilateral whose vertices are on a circle

• inscribed triangle a triangle whose vertices are tangent to a circle

If a right triangle is inscribed in a circle then the

hypotenuse is the diameter of the circle.diameter

4x – 14 = 90

HK

GN

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

x = 26

a quadrilateral inscribed in a circle: opposite angles are

supplementary.A B

CD180 CmAm

180 DmBm

z

y

110

85

110 + y =180y = 70

z + 85 = 180z = 95

Find y and z

Practice WSGet in your

groups please.

12 problems

Homework WSDay 21

Inscribed Angles

Choose even or odd problems