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Daily Check. For each circle C, find the value of x . Assume that segments that appear to be tangent are tangent. 1) 2). Math II. UNIT QUESTION: What special properties are found with the parts of a circle? Standard: MM2G1, MM2G2 Today’s Question:

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slide1

Daily Check

For each circle C, find the value of x. Assume that segments that appear to be tangent are tangent.

1) 2)

math ii
Math II

UNIT QUESTION: What special properties are found with the parts of a circle?

Standard: MM2G1, MM2G2

Today’s Question:

What is the relationship of an inscribed angle to the measure of its intercepted arc?

Standard: MM2G3.b

slide3

6.4

Inscribed Angles

slide4

Inscribed Angle: An angle whose vertex is on the circle and whose sides are chords of the circle

INTERCEPTEDARC

INSCRIBEDANGLE

slide5

YES CL

C

T

O

L

Determine whether the angle is an inscribed angle. Name the intercepted arc for the angle.

1.

slide6

NO; QVR

Determine whether each angle is an inscribed angle. Name the intercepted arc for the angle.

2.

Q

V

K

R

S

slide8

What do we call this type of angle?

What is the value of x?

What do we call this type of angle?

How do we solve for y?

The measure of the inscribed angle is HALF the measure of the inscribed arc!!

120

x

y

examples

J

K

Q

S

M

Examples

3. If m JK = 80, find mJMK.

40 

4. If mMKS = 56, find m MS.

112 

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Q

D

3

J

T

4

U

Example 5

In J, m3 = 5x and m 4 = 2x + 9.

Find the value of x.

x = 3

slide12

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

180

diameter

slide13

Example 6

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

slide14

Example 7

In K, m1 = 6x – 5 and m2 = 3x – 4. Find the value of x.

6x – 5 + 3x – 4 = 90

H

2

K

x = 11

N

1

G

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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.

slide17

A circle can be circumscribed around a quadrilateral if and only if its opposite angles are supplementary.

B

A

D

C

slide18

Example 8 Find y and z.

z

110

110 + y =180

y

y = 70

85

z + 85 = 180

z = 95