
A line, ray, or segment is a tangent of a circle if and only
if
it is in the same plane as the circle and is perpendicular to a radius of the
circle at the point of intersection. 
The measure of an inscribed angle is equal to half the measure
of the intercepted arc. 
In a circle or in congruent circles, inscribed angles that intercept
the same arc or congruent arcs are congruent. 
The measureof an angle formed by a tangent and a chord is equal
to half the measure of the intercepted arc. 
The measure of an angle formed by the intersection of two tangents,
two secants, or a secant and a tangent, at a point outside a circle,
is half the difference of the measures of the intercepted arcs. 
The measure of an angle formed by chords is equal to half the
sum of the measures of the intercepted arcs. 
The perpendicular bisector of a chord passes through the center
of the circle. 
Adiameter that is perpendicular to a chord bisects the chord
and its corresponding arc. 
If two chords intersect inthe interior of a circle,
then the product of the lengths of the segments of one chord is equal to
the product of the lenghts of the segments of the other chord. 
If two secant segments are drawn to a circle from an exterior
point
then the product of the lengths of one secant segment and its external
segment is equal to the product of the lengths of the secant segment and
its external segment. 
If a tangent segments and secant segment circle are drawn to
a circle from an exterior point,
then the product of the lengths of the secant segment and its external
segment is equal to the square of the length of the tangent segment. 
If two tangent segments are drawn to a circle from an exterior
point, then the lengths of the tangent segments are equal. 
If x represents the measure of an arc of a sector and r is the
radius of the circle then the area of the sector is x/360 * (pi)
* r^2. 
If x represents the measure of an arc and r is the radius of
the circle, then the length of the arc is x/360 * 2(pi)r. 