Unit 6 - Circles

Radius

a segment whose endpoints are the center and any point on the circle

Chord

a segment whose endpoints are on a circle

diameter

a chord that contains the center of the circle

Secant

A line that intersects a circle in two points

Tangent

A line in the plane of a circle that intersects the circle in exactly one point.

point of tangency

the point where a circle and a tangent intersect

Arc

a portion of the edge of the circle

Minor Arc

an arc that measures less than 180 degrees

Major Arc

an arc that measures greater than 180 degrees

Semicircle

an arc with endpoints that are the endpoints of a diameter

Central Angle

an angle whose vertex is the center of the circle

inscribed angle

an angle whose vertex is on the circle and whose sides pass through the endpoints of the arc

intercepted arc

The arc that lies in the interior of an inscribed angle and has endpoints on the angle.

arc measure

The measure of the central angle that intercepts an arc, measured in degrees.

tangent segment

a line segment that lies on a tangent line with one endpoint at the point of tangency

Tangent circles

circles that are tangent to the same line at the same point

inscribed polygon

A polygon in which all of the vertices lie on a circle

circumscribed circle

the circle that contains the vertices of an inscribed polygon

cyclic quadrilateral

A quadrilateral that can be inscribed in a circle

A tangent to a circle is \____________ to the radius drawn from the point of tangency

perpendicular

Tangent segments to a circle from a point outside the circle are

congruent

Congruent chords form congruent ?

arcs

If a diameter of a circle is perpendicular to a chord, then the diameter \___?\_____ the chord and its arc.

bisects

Two chords are congruent if they are \____?\_____ from the center

equidistant

The perpendicular bisector of a chord passes through the \___?\____ of the circle

center

If two chords in a circle are congruent, then they determine two central angles that are \___?\_____

congruent

the measure of an angle inscribed in a circle is

one

inscribed angles that intercept the same arc are

congruent

Angles inscribed in a semicircle are

right angles

The opposite angles of a cyclic quadrilateral are

supplementary

parallel lines intercept \___?\___ arcs on a circle

congruent

if two chords interest inside a circle, then the measure of each angle is

one

If a tangent and a secant, two tangents, or two secants intersect outside a circle, then the measure of the angle formed is

one

If two chords intersect in the interior of a circle

then the product of the lengths of the segments is equal to the product of the lengths of the segments of the other chords.

If two secant segments share the same endpoint outside a circle

then the product of lengths of one secant segment and its external secant segment equals the product of the lengths of the other secant segment and its external segment

Circumference

the perimeter of a circle, the distance around the circle

Pi

The ratio of the circumference of a circle to its diameter

Length of an arc

(central angle/360) x 2πr

angular velocity

rate of change with respect to time (degrees per unit of time)

tangential velocity

The speed of an object at a point as it moves around the circumference of a circle (measure of length per unit of time)