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Chapter 10 Circles

Terms in this set (38)

Circle
All the points in a plane equidistant from a given point called the center
Chord
Any segment with endpoints on the circle
Diameter
A chord that passes through the center of the circle
Radius
Any segment with its endpoints as the center of a circle and a point on the circle.
Circumference
The distance around a circle
Π (pi)
The irrational number created by the division of the circumference by the diameter's length of a circle. Approximate faction is 22/7
Central Angle
An angle with its vertex as the center of a circle. (Measure of the central angle is the measure of the arc it intercepts) A group of central angles with no points in common add up to 360
Arc
Part of a circle. Measure of whom can be determined by the measure of the central angle who intercepts it.
Minor Arc
A minor arc's measure is 0<x<180 and is named by its two endpoints.
Major Arc
A major arc's measure is 180<x<360 and is named by its two endpoints and a random point in the arc.
Semicircle
The measure of a semicircle is 180 and is named by its two endpoints and a random point in the arc.
x = y
(congruent arcs and their central angles) Theorem says that in circle A...
mArcAB + mArcBC = mArcAC
Arc Addition Postulate
mc/360 = l(m/360 = I/c)
Arc length Formula
m = arc measure (degrees)
l = arc length
c = circumference
x = y
(Congruent arcs and their corresponding chords) theorem says that in circle A...
Inscribed
____ polygons have all of their vertices on a circle. ____ circles have a point tangent to each side of a polygon.
Circumscribed
___ polygons have a circle with points tangent to each of its sides. ___ circles have all of the vertices of a polygon on it.
diameter
(Diameters or Radii Perpendicular to Chord) theorem converse says that in this circle, a is a...
x = y
(Diameters or radii perpendicular to chords) theorem says that in circle A...
a = b
(Distance of congruent chords from the center in a circle) theorem says that in circle A...
Inscribed Angle
An angle with the vertex on a circle and whose secants intersect the circle again on the circle
x = 15
The Inscribed Angle Theorem says that in circle A...
x = y
(Inscribed angles of the same arc) theorem says that in circle A...
BCD is a semicircle
The (right inscribed angle) theorem says that in circle A...
180
(Circumscribed Quadrilateral's Opposite Angles) Theorem says that in circle A, x + y =
tangent
A line, segment or ray that intersects a circle in exactly one point
Point Of Tangency
The point where a tangent intercepts a circle
b is perpendicular to c
(Tangent and Radius) theorem says that in circle A...
b = c
(Snow-cone) Theorem says that in circle A...
Secant
A line that intersects a circle in 2 points
0.5[mArcBC + mArcED]
(Half The Sum) Theorem says that in circle A, m<EFD =
2m<CBD 2m<CBE
(Just Half) Theorem says that in circle A, ArcCB = __ and ArcCFB = __
x = b - a
(Half The Difference) Theorem says that in circle A...
[BF][FD] = [EF][FC]
(Inside Intersecting Chords) Theorem says that in circle A...
[BC][BD] = [BE][BF]
(Outside Intersecting Secants) Theorem says that in circle A...
BC^2 = [BD][BE]
(Outside Intersecting Tangent And Secant) Theorem says that in circle A...
x + y = 180
(Tangent Snow-cone and Arc) theorem says that in circle A...
(x - h)^2 + (y - k)^2 = r^2
Equation of a circle (All points on a circle can be plugged in to make the equation true.
x = x coordinate of point
y = y coordinate of point
h = center's x coordinate
k = center's y coordinate
r = radius length
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