Geo.Circle#1

• Circle


  The set of all points in a plane that are at the same distance from a fixed point called the center
• Naming a circle


  A circle is named by its center
• Circle on the right

  • Circle O or ⊙O
• Terms associated with circles

  • Radius
  • Central angle
  • Arc
  • Semicircle
  • Minor arc
  • Major arc
• Central angles


  • ∠AOB, ∠BOC
• Minor arcs


  • ,
• Major arcs


  • 
    
• Terms associated with circles

  • Chord
  • Diameter
  • Secant
  • Tangent
  • Point of tangency
• Chords


  • ,
• Diameter

  • 
    
• Secant

  • 
    
• Tangent


  • Point P
• Inscribed polygon


  A polygon all of whose sides are chords of a circle
• Circumscribed circle


  A circle passing through each vertex of a polygon
• Circumscribed polygon


  A polygon all of whose sides are tangents to a circle
• Inscribed circle


  A circle to which all the sides of a polygon are tangents
• Circle Principle 1


  A diameter divides a circle into two equal parts
• Given: AB is a diameter


  arc ACB ≅ arc ADB
• Given: arc ACB ≅ arc ADB

  AB is a diameter
• Circle Principle 2


  Radii of the same or congruent circles are congruent
• Given: OA, OB, OC and OD are radii of ⊙O

  OA ≅ OB ≅ OC ≅ OD
• Circle Principle 3


  Diameters of the same or congruent circles are congruent
• Given: AB and CD are diameters of ⊙O

  AB ≅ CD
• Circle Principle 4


  In the same or congruent circles, congruent central angles have congruent arcs
• Given: ∠1 ≅ ∠2


  arc AC ≅ arc BC
• Given: arc AC ≅ arc BC


  ∠1 ≅ ∠2
• Circle Principle 5


  In the same or congruent circles, congruent chords have congruent arcs
• Given: AB ≅ AC


  arc AB ≅ arc AC
• Given: arc AB ≅ arc AC

  AB ≅ AC
• Circle Principle 6


  A radius/diameter perpendicular to a chord bisects the chord and its arcs
• Given: CD ⏊ AB

  AE ≅ BE, arc AE ≅ arc BE
• Given: AE ≅ BE


  CD ⏊ AB
• Given: arc AE ≅ arc BE


  CD ⏊ AB
• Circle Principle 7


  In the same or congruent circles, congruent chords are equally distant from the center
• Given: AB ≅ CD

  OE ≅ OF
• Given: OE ≅ OF


  AB ≅ CD