Geo.Circle#1

Created by

Jungwoon Yang

Cards (36)

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