Hell is Made of Circles

Circle

The set of all points in a plane that are equidistan from a fixed point called the center

Radius

A segment that joins the center to a point on the circle

Diameter

A chord that passes through the center of the circle (Twice the radius)

Congruent Circles

Two circles are congruent if they have the same radii

Cocentric Circles

Two or more coplanar circles with the same center

Exterior of a Circle

A point on a circle if its distance from the center is greater than the radius

Interior of a Circle

A point inside a circle if ts distance from the center is less than the radius

On the Circle

A point on a circle if tis distance from the center is equal to the radius

Tangent

A line intersecting the circle at exactly one point

Secant

A line intersecting the circle in exactly two points

Tangent Radius Theorem

A tangent line is perpendicular to the radius drawn at the point of tangency

Tangent Radius Theorem Converse

A line perpendicular to a radius at its outer end point, then it is a tangent to the circle

Central Angle

An angle whose vertex is at the center of the circle

Arc

Consists of two points on a circle and all points on that needed to connect the points by a single path. The center of the arc is the same center of the circle

Minor Arc

The shortest arc connecting two endpoints on a circle

Major Arc

The longest arc connecting two endpoints on a circle

Semicircle

An arc where its endpoints lie on the diameter

Congruent Arcs

Two arcs are congruent whenever they have the same measure adna re parts of the same circle or congruent circles

Relating Chords, Arcs, and Central Angles

If two central angles are congruent, then the chords and arcs are also congruent; converse is also true

Chord

A segment joining any two points on the circle

Chord Theorem 1

If a radius is perpendicular to a chord, then it bisects the chord.

Chord Theorem 2

If a radius of a circle bisects a chord that is not a diameter, then it is perpendicular to that chord

Chord Theorem 3

The perpendicular bisector of a chord passes through the center of the circle

Chord Theorem 4

If two chords of a circle are equidistant from the center then they are congruent

Chord Theorem 4 Converse

If two chords of a circle are congruent, then they are equidistant from the center

Common Tangent

A line tangent to two circles

Common Internal Tangent

Crosses the Line of Centers

Common External Tangent

Does not cross Line of Centers