2 6 8 5 5 8

62x 2x 3x

92

88

176

x

y

z

a 90b 28c 56

66

54

120

a

b

c

7.7

What More Can I Learn About Circles?

Pg. 24

Angles Inside and Outside Circles

7.7 – What More Can I Learn About Circles? Inside and Outside Circles

So far you have investigated when an angle is formed at the center or the side of the circle. Today you are going to continue to find angle measures that are inside and outside of circles.

7.35 –ANGLE LOCATION Determine if the angle formed is inside, outside, at the center, or on the circle.

.

on center inside outside

7.36 – INSIDE ANGLESUri now has a challenge for you: What happens when chords intersect inside a circle? Discover the relationship between the inside angle and the two intercepting arcs.

½a ½b

180-½a-½b

½a + ½b

x = a + b

2

x = arc + arc2

If an angle is formed inside of a circle not at the center, then the angle is ________ the ___________ of the two intercepted arcs.

half

sum

vertical

Inside angle = arc + arc 2

7.37 – EXTRA PRACTICEUsing the information you have learned, find the missing variables.

x°

x = 86 + 882

x = 1742

87x

x = 120 + 982

x = 2182

109x

7.38 – OUTSIDE ANGLESUri now has a new challenge for you: What happens when secants and tangents intersect outside a circle?

ab

½ b

½ a

180 – ½b x°

x + ½ a + 180 – ½ b = 180x + ½ a – ½ b =

0 x = ½ b – ½ a

x =

b – a 2

x =

Big arc – little arc 2

b a x

http://www.cpm.org/flash/technology/sectangent.swf

If an angle is formed outside of a circle, then the angle is  ________ the ________________ of the two intercepted arcs.

halfdifference

Outside angle = big arc – little arc 2

7.39 – EXTRA PRACTICEUsing the information you have learned, find the missing variables.

x °

y ° x

°

x = B – L2

x = 90 – 202

x = 702

x = 35°

41°

y = B – L2

y = 111 – 412

y = 702

y = 35°

56°B – L

2

134 – 562

782

39°

2

117°

x = B – L2

x = 243 – 1172

x = 1262

x = 63°