CIrcles

Central angle

Central angle

An angle coming outward from the center of a circle

Arc

is a part of the circumference of a circle which a center angle lies on.(measure is the measure of the central angle)

Arc addition postulate

The measure of an arc formed by 2 adjacent arcs is the measure of the 2 arcs.(eg:mABC= mAB+mBC)

congurent arcs therom

• if 2 circles radiuses are equal then both circles are congruent

• if arcs are congruent then both central angles are congruent

Congruent corresponding chords therom

2 minor arcs are equal only if both chords are congruent

perpendecular chord bisector therom

if there is a right angle then the arc and chord are split (there is a chord and the diameter splits it into 2 arcs and chords)

perpendecular chord bisector converse

if an arc and a chord are bisected then there is a right angle

equadistant chords therom

2 chords are congruent only if they are equadistant from the center .(for 2 chords to be equal the distance from the center) eg: chord AB and CD are equal because they are both 4 inches away from the center.

Tanget intercepted chord therom

if a tanget chord intercepts at a point on a circle then the measure of each angle formed is half of the measure of its intercepted arc.

3 places a line can be intercepted at…

outside the circle,inside the circle,on the circle

Angles inside the circle therom

if 2 chords intercept a circle then the measure of each angle is half the sum of the measure of the chords( 2 chords intersect inside of a circle and both measure up to 234 so the angle formed by this intersection would be 117 degrees)

segments of a circle therom

if 2 chords intercept in the interior of a circle,then the product of the lengths of the segmants of one chord is equal to the product of the lengths of the segments of the other chord.(eg:chord AB and CHord DC intercect and form point E.

(EA x EB = EC x ED.)

Angles outside of a circles therom

if a tanget and a secant,or 2 of each intercept outside of a circle then the angle formed is half the difference between both intercepted arcs(eg: a secant and a tanget line both intercet a circle and form a angle outside of it, one arc measures 100 while the other measures 140 so the angle formed would be 20 because 40 is the difference between 100 and 140 then half it)

circumscribed angle therom

the measure of a circumscribed angle is 180-central angle that intercepts the arc(eg:a central angle is 135 so the circumscribed angle to that is 180-35 so 45 Is your circumscribed angle)

insicribed(inside) right triangle therom

if a right triangle is inscribed(inside) in a circle,then the hypotanous is the diameter of the circle)

inscirbed(inside) quadrerlateral therom

a quadrerlateral can only be inscribes(inside) a circle if its opposite angles are supplementary(add up to 180)

segmants of secants and tangents therom

if a secant segment and a tangent segment share an endpoint outside of a circle then the product of the lengths of the secant segment x its external segment is equal to the square of the length of a tangent segment (EC(outside segment) x ED(entire secant segment) = EA²)

tanget segment

a segment that is tanget( touching only one point of a circle) to a circle at an endpoint

secant segment

a segment that contains a chord of a circle and has exactly one endpoint outside of the circle(the outside segment of a secant is called a external segment)

segments of scents therom

if 2 segments share the same endpoint outside a circle,then the product of the lengths of secent segment x the length of the external segment is equal to the other secant segment x its external segment.(secent segments EAB and ECD meet at point E so EA x EB = EC x ED)

standered circle form

(x-h)² +(y-k)² =r²

(h,k) are the center coordinates

circumference of a circle…..

2πr

area of a circle……

πr²