Other Angle Relationships In Circles

GeometryChapter 10

A BowerPoint Presentation

2 chords

• Draw 2 intersecting chords in your circle• Label a pair of vertical angles as angles 1

and 2• What do you know about angles 1 and 2?

2 chords

• Draw 2 intersecting chords in your circle• Label a pair of vertical angles as angles 1

and 2• What do you know about angles 1 and 2?

– They are congruent!

2 chords

• Angles 1 and 2 intercept two different arcs of the circle. Do these arcs have to be congruent?

2 chords

• Angles 1 and 2 intercept two different arcs of the circle. Do these arcs have to be congruent?– No!

2 chords

2 chords

2 chords

• Find the measures of angles 1 & 2

2 chords

• Find the measures of angles 1 & 2

Both angles = 110o

2 chords

• Find x

2 chords

• Find x

x = 80

2 secants

• Put a point outside the circle (probably to the right)

• Draw two secants that go through that point and through the circle

• Do you see how the angle you’ve created intercepts two arcs in the circle?

2 secants

2 secants

2 secants

• Find the measure of angle 1

2 secants

• Find the measure of angle 1 Angle 1 = 50o

2 secants

• Find x

2 secants

• Find x x = 130

1 secant & 1 tangent

• Put a point outside the circle (probably to the right)

• Draw a secant that goes through the circle and through the point

• Draw a tangent that touches the circle at one point and goes through your point

• Do you see how the angle you’ve created intercepts two arcs in the circle?

1 secant & 1 tangent

1 secant & 1 tangent

1 tangent & 1 secant

• Find the measure of angle 1

1 tangent & 1 secant

• Find the measure of angle 1 Angle 1 = 45o

1 secant & 1 tangent

• Find x

1 secant & 1 tangent

• Find x x = 90

2 tangents

• Put a point outside the circle (probably to the right)

• Draw two tangents that each touch the circle once and intersect at your point

• Do you see how the angle you’ve created intercepts two arcs in the circle?

2 tangents

2 tangents

2 tangents

• Find the measure of angle 1 (There is enough information!)

2 tangents

• Find the measure of angle 1 (There is enough information – how big is green arc?)

2 tangents

• Find the measure of angle 1 Angle 1 = 80o

2 tangents

• Find x

2 tangents

• Find x x – (360 – x) = 2 (50)

2 tangents

• Find x x = 230