Arcs and Angles Flashcards
Circle
A set of all points in a plane that are equal at distance from the center
Radius
A segment whose endpoints are on the circle & any point on the cirlce(half the diameter)
Diameter
Chord that contains the center of the circle
Chord
Segment whose endpoints are on a circle
Secant
A line that intersects the circle in 2 points
Tangent
A line on the outside(edge) of cirlce that intersects at 1 point
Point of Tangency
The point the tangent line creates
Tangent Circles
Coplanar circles that intersect in one point
Conectric Circles
Coplanar Circles that have a common center
Circular Arc
Part of a circle
Minor Arc
Less than 180 degrees
Major
More than 180 degrees
Semi-Circle
Half of the cirlce (equal to 180 degrees)
Acr Addition Posulate
The measure of an arc formed y two adjancent ars is the sum of the measures of the two arcs (mABC=mAB+mBC)
Congruent Corresponding Chords Theorem
Inthe same circle, or in congruentcircles, twominor arcs are congruents if and only if their corresponding chords are congruent
Perpindeicular Chord Bisector Theorem
If a diameter of a circleisperpindicular to a chord, then the diameter bisects the chord & arc
Perpendicular Chord Bisector Converse
If one of a circle isa perpendicualr bisector of another chord, thenthe first chord is a diameter
Equidsant Chords Theorem
In the same circle, or in congruent circles, two chords are congruent if & only if they are equidsant from center
Inscribed Angle
An angle whose vertex is on a circle & whose sides contain chords of the circle
Intercepted Arc
Anarc that lies between two lines, rays, or segements
Subtend
Endpoints of a chord or arc lie on the sides of an inscribed angle, then the chord or arc
Inscribed Polygon
All pf the polygons vertices lie on a circle
Circumscribed Polygon
Circle that contains the vertices
Tangent & Intersected Chord Theorem
If a tangent & chord intersect at a point on a circle, then the measure of each angle formed is one-half the measure of its intercepted arc
(m<1= 1/2mAB)
Angles inside the Circles Theorem
If two chords intersect inside a circle, then the measure of each abgle is one-half the sum of the measure of the arc intercepted by the angle & its vertical angle
m<1=1/2(mDC+mAB)
Angles Outside the Circle Theorem
If a tangent and a secant, two tangents, or two secants intersect outside a circle, the the measure of the angle formed is one-half the difference of measures of the intercepted arcs
m<1= 1/2(mBC-mAB)
Segment of the Chord
When 2 chords intersect in the interiorof a circle each chord is divded into2 segments
Segments of Chord Theorem
If 2 chords intersect in the interior of a circle,then the product of the lengths of the segments of one chord is equal to the product ofthe lengthd of the segments of the other chord
(EAEB=ECED)
Tangent Segment
A segment that is tangent to a circle at an endpoint
Secant Segment
A segment the containsof a circle& has exactly one endpoint outside the circle
External Segment
The part of a secant segment that is outside the circle
Segments of Theorem
If two secant segments share the same endpoint outside a circle, then the product of the lengths of one secant segment & its external segments equals the product of the lenghs of the other secant segment & its external segment
(EAEB=ECED)
Standard Equation of a Circle
(x-h)^2 + (y-k)^2 = r^2
