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Other Angle Relationships In Circles . Geometry Chapter 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 - PowerPoint PPT Presentation
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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