Circles

Question 1

circumferene

Answer 1

pi x diameter

Question 2

area

Answer 2

pi x radius x radius

Question 3

length of arc

Answer 3

(central angle/360) x circumference

Question 4

area of sector

Answer 4

(central angle/360) x area of circle

Question 5

concentric circles

Answer 5

circles with same center

Question 6

radius-chord theorems4

Answer 6

• 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

Question 7

congruent chords

Answer 7

chords that are equidistant from the center (perpendicular bisectors congruent)

Question 8

central angle

Answer 8

angle whose vertex is at the center of a circle

Question 9

minor arc

Answer 9

arc whose points are on/between sides of a central angle

Question 10

major arc

Answer 10

arc whose points are on/outside sides of a central angle

Question 11

semicircle

Answer 11

arc whose endpoints are the endpoints of the diameter

Question 12

secant

Answer 12

line that intersects a circle at exactly two points (contains a chord)

Question 13

tangent

Answer 13

line that intersects a circle at exactly 1 point, perpendicular to radius

Question 14

tangent segment

Answer 14

part of tangent line between point of contact and point outside circle

Question 15

secant segment

Answer 15

part of secant line that joints a point outside the circle to the farther intersection point of the line and the circle

Question 16

external part of secant segment

Answer 16

part of secant line that joins outside point to nearer intersection point

Question 17

two-tangent theorem

Answer 17

if two tangent segments are drawn to a circle from an external point, then those segments are congruent

Question 18

externally tangent circles

Answer 18

circles that intersect at 1 point outside each other

Question 19

internally tangent circles

Answer 19

one circle lies inside other and intersects at one point

Question 20

line of centers

Answer 20

line connecting centers of both tangent circles where point of contact falls on

Question 21

common tangent

Answer 21

line tangent to two circles

Question 22

common external tangent3

Answer 22

• doesnt lie bewteen circles,
• doesnt intersect line of centers
• CETs of two circles are congruent

Question 23

common internal tangent2

Answer 23

• lies between the circles

- intersects line of centers

Question 24

find common tangent5

Answer 24

• 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

Question 25

angles equal to arc

Answer 25

-central angles: vertex in center

Question 26

angles half the arc2

Answer 26

• 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

Question 27

angles half sum of arcs

Answer 27

-chord-chord angles: vertex inside circle not at center

Question 28

angles half difference of arcs3

Answer 28

• 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

Question 29

angle arc theorems3

Answer 29

• 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

Question 30

inscribed polygon

Answer 30

inside circle (vertices lie on circle)

Question 31

circumscribed polygon

Answer 31

outside circle (sides are tangent to circle)

Question 32

circumcenter

Answer 32

center of a circle circumscribed about a polygon (an inscribed polygon)

Question 33

incenter

Answer 33

center of a circle inscribed about a polygon (an circumscribed polygon)

Question 34

power theorems3

Answer 34

• 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

Question 35

circle equation

Answer 35

(x-h)squared + (y-k)squared = radius squared

(-h,-k) is center, r is radius