10.4 Other Angles Relationships In Circles. Theorem A tangent and a chord intersect at a point, it...

14
10.4 Other Angles Relationships In Circles

Transcript of 10.4 Other Angles Relationships In Circles. Theorem A tangent and a chord intersect at a point, it...

Page 1: 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.

10.4 Other Angles Relationships In Circles

Page 2: 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.

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

Page 3: 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.

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

Page 4: 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.

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

Page 5: 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.

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

Page 6: 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.

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

Page 7: 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.

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

Page 8: 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.

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

Page 9: 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.

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

Page 10: 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.

Theorem

Two tangents make two intercept arc, the angle made is

½ ( the big arc minus the small arc)

½(arcACB-arcAB)Pm

100C

Page 11: 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.

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

Page 12: 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.

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

Page 13: 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.

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

Page 14: 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.

Homework

Page 624 – 627

# 8 – 34, 42,

46, 47, 49 – 51

Thank you http://literacy.calumet.purdue.edu/student/bakerl3/10_5tutorial.html


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