Circles

Center

Equidistant from all circle points

Radius

Segment with a center to edge endpoint

Chord

Segment with endpoints on the circle

Diameter

A chord that has the center

Secant

A line that intersects a circle in 2 points

Tangent

A line that intersects the circle in 1 point

Congruent circles

Circles that have congruent radii

Common Tangent

Line that is tangent to 2 circles

Tangent Line to Circle theorem

A line is tangent to a circle only if the line is perpendicular to the radius

External Tangent Congruence Theorem

Tangent segments from a common exteranal point are congruent

Measure of Minor Arc

central angle under 180

Measure of major arc

360-minor arc, over 180

Arc Addition Postulate

1 big arc = sum of 2 composing arcs

Congruent circles theorem

2 circles are congruent if they have the same radius

Congruent central angles theorem

In the same or congruent circles 2 minor arcs are congruent if their central angles are congruent

Similar arcs

2 circles that have the same measure

all congruent arcs are similar but not all similar arcs are congruent

Similar circles theorem

All circles are similar

Congruent Corresponding Chords Theorem

In same or congruent circle, 2 minor arcs a congruent if their corresponding chords are congruent

Perpendicular Chord bisector theorem

If the diameter is perpendicular to a chord then the diameter bisects the chord

Perpendicular Chord Bisector Converse

If 1 chord is a perpendicular bisector of another chord then the first is a diameter

Equidistant Chords theorem

In the same or congruent circles, 2 chords are congruent if they are equidistant from the center

Inscribed Angle

An angle with the vertex on circle and sides contain chords

Intercepted Arc

Arc that is between 2 segments

Measure of an inscribed angle theorem

Measure of the angle is half the arc

Inscribed Angles of a Circle Theorem

If 2 inscribed angles intercept the same arc the angles are congruent

Inscribed Polygon

When all the vertices are on the circle

Circumscibed Circle

A circle that contains the polygon vertices

Inscribed Right Triangle theorem

If a right triangle is in the circle then the hypotenuse is the diameter

If one side is a diameter then in is a right triangle

Inscribed Quadrilateral Theorem

A quadrilateral can only be in a circle if the opposite angles are supplementery

Square, Rectangle, Isoceles Trapazoid

Tangent and Intersected Chord Theorem

When a tangent and chord intersect, the measure of each angle formed is half its intercepted arc

Angles Inside the Circle Thorem

In 2 chords intersects inside a circle then the measure of each angle =

half the sum arc intercepted by its vertical angle

Angles Outside the Circle Theorem

If a tangent or secant intersect outside the circle then the angle measure is

half the difference of the intercepted arcs

Circumsciribed Angle

Angle with tangent sides to circle

Circumscibed Angle Theorem

Circumscribed angle = 180 - same central angle

Segments of Chords Theorem

If 2 Chords intersects inside a circle then the Product of there segemnts is equal to the other chord

Segments of Secants Theorem

If 2 secant segments share the same endpoint outside the circle then the

Whole segment x external segment is equal to eachother

Segments of Secants Theorem and Tangents

If a tangent and secant share the same endpoint the

Tangent squared = Whole secant x external part