Circles not on a plane

circle

A geometric figure consisting of all the points on a plane that are the same distance from a single point.

center of a circle

the exact center of a circle, all points same distance from this point

Radius

A line segment that as one endpoint at the center of the circle & the other endpoint on the circle

Circumference

The distance around the circle

Chord of a circle

Any line segment whose end points are on a circle (shortest distance to center is the perpendicular bisector Which is also a radius)

If two chords are congruent,

they MUST be the same distance from the center of the circle

Diameter

A chord that passes through the center of the circle, x2 the radius, longest chord of a circle

Arc

A part of a circle between two points on the circle

central angle

an angle that has its vertex at the center of a circle; formed by two line segments that connect the center of a circle to the endpoints of an angle. (CONGRUENT TO THE ARC IT INTERSECTS)

Minor Arc

An arc of a circle that is shorter than half the circumferencem less than 180

Major arc

An arc of a circle that is longer than half the circumference, greater than 180

Two arcs are congruent if,

-they have the same length & belong to the same circle or two congruent circles

• their associated chords are congruent

two chords are congruent if,

the associated center angles are congruent

Inscribed angle

An angle formed by two chords that share an endpoint, half the measure of the arc it intercepts

inscribed angle theorem

The measure of an inscribed angle is always half the measure of its intercepted arc

intersecting chords theorem

intersecting chords form a pair of congruent vertical angles

secant

a straight line or segment that passes through a circle at two points

secant secant Angle

an angle formed by the intersection of two secants of the same circle

Tangent

A line that intersects a circle at exactly one point, perpendicular to the radius that shares a point, half the measure of the intercepted arc

tangent tangent angle

An angle formed by intersecting tangents, half the difference of intercepted arcs

circumference formula

2πr

to find arc length formula

length of arc = 2πr x( length of arc/ 360)

Area of a circle formula

πr²

Sector

A part of the interior of a circle bounded by an arc and the two radii that share the arc’s end points

Area of sector formula

πr² x measure of arc

Inscribe

to fit one object tightly inside another

Incenter

The intersection of the angles bisector is the incenter, always on the inside

features of an incenter

• center of only circle that can be inscribed inside a triangle

• equidistant from all SIDES

• bisectors intersect

• CIRCLE IN TRIANGLE

Circumscribed

fit tightly around

circumcenter of a triangle

the center of the only circle that can be circumscribed around a given triangle

features of a circumcenter

• equidistant from VERTICES

• perpendicular bisectors (so inside outside rules apply)

• CIRCLE AROUND TRIANGLE

Polygons that can be circumscribed in a circle

• rectangle

• triangle

• square

a parallelogram that can be inscribed in a circle

a rectangle

opposite angles of a quadrilateral in a circumscribed circle are

supplementary