10.4 Other Angles Relationships In Circles

Theorem

A tangent and a chord intersect at a point, it makes angles that are ½ the intercepted arc.

12

X

YZ

XZm

XYZm

2

11

2

12

Theorem

A tangent and a chord intersect at a point, it makes angles that are ½ the intercepted arc.

12

X

YZ

XZm

XYZm

2

11

2

12

120

?2

?1

m

m

Theorem

A tangent and a chord intersect at a point, it makes angles that are ½ the intercepted arc.

12

X

YZ

XZm

XYZm

2

11

2

12

120

1202

601

m

m

240

Theorem

If two chords intersect in the circle, then the angles made are ½ the sum of the intercept arcs.

3

yxm2

13

9560

?3m

Theorem

If two chords intersect in the circle, then the angles made are ½ the sum of the intercept arcs.

3

yxm2

13

9560

5.773m

1552

13

95602

13

m

m

Theorem

A tangent and a secant make two intercept arc, the angle made is

½ ( the big arc minus the small arc)

½(arcAC-arcBC)Pm

Theorem

A tangent and a secant make two intercept arc, the angle made is

½ ( the big arc minus the small arc)

½(arcAC-arcBC)Pm

40

160

Theorem

A tangent and a secant make two intercept arc, the angle made is

½ ( the big arc minus the small arc)

½(arcAC-arcBC)Pm

40

160

60

1202

1

401602

1

Pm

Pm

Pm

Theorem

Two tangents make two intercept arc, the angle made is

½ ( the big arc minus the small arc)

½(arcACB-arcAB)Pm

100C

Theorem

Two tangents make two intercept arc, the angle made is

½ ( the big arc minus the small arc)

½(arcACB-arcAB)Pm

100C

80

1602

1

1002602

1

Pm

Pm

Pm

Theorem

Two secants make two intercept arc, the angle made is

½ ( the big arc minus the small arc)

½(arcAC - arcBD)Pm 100

20

Theorem

Two secants make two intercept arc, the angle made is

½ ( the big arc minus the small arc)

½(arcAC - arcBD)Pm 100

20

40

802

1

201002

1

Pm

Pm

Pm

Homework

Page 624 – 627

# 8 – 34, 42,

46, 47, 49 – 51

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