Circle Unit

Standard Form for a Circle at Origin

x²+y²=r²

Standard Form at center (h, k)

(x-h)²+(y-k)²=r²

radius

line SEGMENT from the center to a point on the circumference

diameter

a chord that passes through the center of a circle

Circles are similar through

dialation and translation

Circle

set of all points that are the same distance from the center point

Chord

a line SEGMENT whose endpoints are on the circle

Secant Line

A LINE that intersects the circle twice

Tangent Line

A line that touches the circle once.

Tangent Point

Where the tangent line touched the circle

arc

piece of the circumference

Sector

piece of the area of the circle

Central Angle

An angle with the center as its vertex

Inscribed Angle

An angle with its vertex on the circumference

A radius drawn to a tangeant…

is perpendicular at the point of tangency

the segment from two tangent points to an outside point are…

congruent

a tangent line is perpendicular to…

a radius drawn at the point of tangency

if a line is perpendicular to a radius at its outer endpoint…

it is tangent to a circle

the angle formed by a tangent and a chord is half…

the measure of the arc in between the endpoints of the chord

the measure of a central angle is…

the SAME as the measure of its arc

the measure of an inscribed angle is…

HALF the measure of its intercepted arc

Inscribed angles that intercept the same arc are…

congruent

an inscribed angle within a semi-circle is

a right angle

an inscribed quadrilateral has opposite angles that are

supplementary

the measure for a major arc is

360 minus the measure of the minor arc with the same endpoints

if two central angles of a circle are congruent…

their intercepted arcs are congruent

if two chords of a circle are equidistant from the center of the circle…

the chords are congruent

if two chords are congruent…

they’re equidistant from the center of the circle

arcs that intercept congruent chords are

congruent

all radii are

congruent

if a radius is perpendicular to a chord…

it bisects the chord.

radians to degrees

Multiply by 180/pi

degrees to radians

Multiply by pi/180

area of a sector (radians)

1/2(θ)(r²)

area of a sector (degrees)

½ (θ(pi/180) (r²)

arc length (radians)

θ(r)

arc length (degrees)

(θ)(pi/180)(r)

the measure of a chord/chord angle is

half the sum of the measures of the arcs intercepted by the angle

the measure of a secant/secant, secant/tangent, or tangent/tangent is

half the difference of the measures of the intercepted arcs