Circle
the set of points in a plane equidistant from a given point (notation: ⊙A, with A being the center)
Center
The fixed point in the center of a ⊙ (notation: A)
Radius
dist from center to a pt. on a circle (segment notation)
Chord
a segment that joins 2 points on the ⊙
Secant
A line that contains a chord
Diameter
A chord that contains the center
Tangent
A line that intersects a circle in exactly one point
Point of Tangency
The intersection point of a tangent to a ⊙
Sphere
A set of points in space equidistant from a fixed point
Congruent spheres / ⊙
Have ≅ radii
Cocentric spheres / ⊙
have the same center
inscribed polygon
All vertices are on the ⊙
Circumscribed circles
⊙ is around the polygon
tangent → ⊥ radius
If a line is tangent to a circle, then it is ⊥ to the radius
ice cream cone corr
Tangents to a circle from a point are ≅
⊥ radius → tangent
If a line in the plane of a circle is perpendicular to the radius at its outer endpoint, then the line is tangent
central angle
an angle whose vertex is on the center of a circle
Arc
an unbroken piece of a circle (minor, major, and semi)
Adjacent arcs
Arcs that have exactly one point in common
Congruent arcs
arcs in the same circle or congruent circles that have equal measure
arc addition postulate
basically SAP but with arcs
2 minor arcs ≅ iff central <s ≅
in the same circle or congruent circles, two minor arcs are congruent if and only if their central angles are congruent.
≅ arcs → ≅ chords, vice versa
in the same circle or congruent circles, congruent arcs have congruent chords, and congruent chords have congruent arcs
diameter ⊥ chord → mdpt & bisects arc
A diameter that is perpendicular to a chord bisects the chord and its arc
chords =dist center → ≅
≅ chords → =dist center
in the same circle or congruent circles, chords equally distant from the center(s) are congruent, and congruent chords are equally distant from the center(s)