Circles Flashcards
circumferene
pi x diameter
area
pi x radius x radius
length of arc
(central angle/360) x circumference
area of sector
(central angle/360) x area of circle
concentric circles
circles with same center
radius-chord theorems4
- distance from center to a chord is measure of perpendicular segment from center to chord
- if a radius bisects a chord thats not a diameter, then its perpendicular to the chord
- if a radius is perpendicular to a chord, it bisects the chord
- the perpendicular bisector of a chord passes through the center of the circle
congruent chords
chords that are equidistant from the center (perpendicular bisectors congruent)
central angle
angle whose vertex is at the center of a circle
minor arc
arc whose points are on/between sides of a central angle
major arc
arc whose points are on/outside sides of a central angle
semicircle
arc whose endpoints are the endpoints of the diameter
secant
line that intersects a circle at exactly two points (contains a chord)
tangent
line that intersects a circle at exactly 1 point, perpendicular to radius
tangent segment
part of tangent line between point of contact and point outside circle
secant segment
part of secant line that joints a point outside the circle to the farther intersection point of the line and the circle
external part of secant segment
part of secant line that joins outside point to nearer intersection point
two-tangent theorem
if two tangent segments are drawn to a circle from an external point, then those segments are congruent
externally tangent circles
circles that intersect at 1 point outside each other
internally tangent circles
one circle lies inside other and intersects at one point
line of centers
line connecting centers of both tangent circles where point of contact falls on
common tangent
line tangent to two circles
common external tangent3
- doesnt lie bewteen circles,
- doesnt intersect line of centers
- CETs of two circles are congruent
common internal tangent2
- lies between the circles
- intersects line of centers
find common tangent5
- draw line of centers
- draw radii to points of contact
- through center of smaller circle, draw a line parallel to common tangent
- extend line to intersect radius to bigger circle, forming a rectangle and right triangle
- use pythagorean theorem and properties of a rectangle to solev
angles equal to arc
-central angles: vertex in center
angles half the arc2
- inscribed angles: vertex on circle and sides are chords
- tangent-chord angles: vertex on circle and one side is a tangent and one side is a chord
angles half sum of arcs
-chord-chord angles: vertex inside circle not at center
angles half difference of arcs3
- secant-secant angles: vertex outside circle and sides are secants
- secant-tangent angles: vertex outside circle and sides are 1 secant and 1 tangent
- tangent-tangent angles: vertex outside circle and sides are tangents
angle arc theorems3
- if two inscribed or tangent-chord angles intercept the same or congruent arcs, then they are congruent
- an angle inscribed in a semicircle is a right angle
- the sum of the measures of tangent-tangent angle and its minor arc is 180
inscribed polygon
inside circle (vertices lie on circle)
circumscribed polygon
outside circle (sides are tangent to circle)
circumcenter
center of a circle circumscribed about a polygon (an inscribed polygon)
incenter
center of a circle inscribed about a polygon (an circumscribed polygon)
power theorems3
- chord-chord: measures of the segments of one chord equals the product of the segments of the other chord
- tangent-secant: square of tangent segment is equal to product of entire secant segment and its external part
- secant-secant: product of one whole segment to its external part is equal to the product of the other whole segment to its external part
circle equation
(x-h)squared + (y-k)squared = radius squared
(-h,-k) is center, r is radius
