7.5

What’s The Relationship?Pg. 18

Inscribed and Central Angles

7.5 – What’s The Relationship?Inscribed and Central Angles

In order to learn more about circles, we need to investigate the different types of angles and chords that are found in circles.

Term Definition Picture

Central Angle

An angle whose vertex is the center of the circle

P

A

C

APC

40

320 320

8080

80

73°73°

73 _______mMN

73°

26°

73°

_______mNQ 107

73°

26°

73°

_______mMP 15481°

73°

26°

73°

_______mMRP 20681°

73°

26°

73°

_______mPN 8181°

73°

26°

73°

_______mMNQ 18081°

73°

26°

73°

_______mMRQ 18081°

73°

26°

73°

_______mMRN 28781°

An angle whose vertex is ON a circle

Inscribed angle:

BDCHalf the intercepted arc

An arc that is inside an inscribed angle

Intercepted Arc:

BCDouble the inscribed angle

2x

2x

x

Half of WZY

8040

4040

F G H

180

90Inscribed angle is half the arc

6

8

36 + 64 = x2

100 = x2

10 = xr = 5

10

62 + 82 = x2

The measures of an inscribed angle is ________ the measure of its ______________ arc.

halfintercepted

D = AB 2x°

2x°

If two inscribed angles of a circle _____________ the same arc, then the angles are _____________.

interceptcongruent

D C

A ________ triangle is inscribed in a circle iff the _______________ is a diameter of the circle.

righthypotenuse

180

90

7.29 – PRACTICEIn the previous problem, you found that the measure of an inscribed angle is always half of the measure of its corresponding central angle. Use this new information to answer the questions below.

59°

82°

56°

28°

114°57°

156°180°

360 156 180z 24

24

40°

20°

360 1002

130

130° 130°

200°

160°

80°

91.5°

183°

212°

106° 73°

74°

42°

42°

90°

45° 45°

130°

118°

59°

x°

x°

x°

2x°

Central angle Inscribed angle