This is a draft cheat sheet. It is a work in progress and is not finished yet.
Vocabulary
interior of a circle 
the set of all points inside the circle 
exterior of a circle 
the set of all points outside the circle 
chord 
a segment whose endpoints lie in a circle 
secant 
a line that intersects a circle at two points 
tangent 
a line in the same plane as a cicle that intersects it at exactly one point 
point of tangency 
the point where the tangent and a circle intersect is called the point of tangency 
common tangent 
a line that is tangent to two circles 
central angle 
an angle whose vertex is the center of a circle 
adjacent arcs 
arcs of the same circle that intersect at exactly one point 
congruent arcs 
two arcs within a circle or two circles that have the same measure 
sector of a circle 
a region bounded by two radii of the circle and their intercepted arc 
segment of a circle 
a region bounded by an arc and its chord 
arc length 
the distance along an arc measured in linear units 
inscribed angle 
an angle whose vertex is on a circle and whose sides contain chords of the circle 
intercepted arc 
consists of endpoints that lie on the sides of an inscribed angle and all the points of the circle between them 
subtends 
a chord or arc subtends an angle if its endpoints lie on the sides of the angle 
Formulas
*m = arc measurement in degrees* 
area of a sector of a circle 
A = 𝜋r^{2}(m/360) 
area of a segment of a circle 
A = area of sector  area of the triangle formed inside the sector 
arc length 
L = 2𝜋r(m/360) 
Angle Relationships in Circles
vertex of the angle 
measure of angle 
on a circle 
half the measure of its intercepted arc 
inside a circle 
half the sum of the measures of its intercepted arcs 
outside a circle 
half the difference of the measures of its intercepted arcs 
Angle Relationships in Circles
vertex of the angle 
measure of angle 
on a circle 
half the measure of its intercepted arc 
inside a circle 
half the sum of the measures of its intercepted arcs 
outside a circle 
half the difference of the measures of its intercepted arcs 


Pairs of Circles
congruent circles 
if and only if they have congruent radii 
concentric circles 
coplanar circles with the same center 
tangent circles 
two coplanar circle that intersect at exactly one point 
Arcs
minor arc 
an arc whose points are on or in the interior of a central angle 
the measure of a minor arc is equal to the measure of its central angle 
major arc 
an arc whose points are on or in the eterior of a central angle 
the measure of a major arc is equal to 360 degrees minus the measure of its central angle 
semicircle 
when the endpoints of an arc lie on a diameter 
the measure of a semicircle is equal to 180 degrees 
Theorems & Postulates
1211 
if a line is tangent to a circle, then it is perpendicular to the radius drawn to the point of tangency 
1212 
if a line is perpendicular to a radius of a circle, then the line is tangent to the circle 
1213 
if two segments are tangent to the same external point, then the segments are congruent 
1223 
in a circle, if a radius (or diameter) is perpendicular to a chord, then it bisects the chord and its arc 
1224 
in a circle, the perpendicular bisector of a chord is a radius (or diameter) 
1241 inscribed angle theorem 
the measure of an inscribed angle is half the measure of its intercepted arc 
1242 
if inscribed angles of a circle intercept the same arc or are subtended by the same chord or arc then the angles are congruent 
1243 
an inscribed angle subtends a semicircle is and only if the angle is a right angle 
1244 
if a quadrilateral is inscribed in a circle, then its opposite angles are supplementary 
1251 
if a tangent and a secant (or chord) intersect on a circle at the point of tangency, then the measure of the angle formed is half the measure of its intercepted arc 
1252 
if two secants or chords intersect in the interior of a circle, then the measure of each angle formed is half the sum of the measures of its intercepted arcs 
1253 
if a tangent and a secant, two tangents, or two secants intersect in the exterior of a circle, then the measure of the angle formed is half the difference of the measures of its intercepted arcs 
Theorem 1222
in a circle or congruent circles... 
1. congruent central angles have congruent chords 
2. congruent chords have congruent arcs 
3. congruent arcs have congruent central angles 
