circle facts pt.1

Question 1

a line segment from the center of a circle to ANY point on the circle

Answer 1

radius

Question 2

line segment whose endpoints are both points on the circle

Answer 2

chord (yay)

Question 3

a chord passing through the CENTER of the circle

Answer 3

diameter

Question 4

a line intersecting the circle in exactly one point (point of tangency), does not touch circle except for this one particular spot

Answer 4

tangent

Question 5

a line intersecting or passing through the circle in 2 different distinct points

Answer 5

secant

Question 6

an angle whose vertex is the center (!) of the circle and whose rays are radii of the circle

Answer 6

central angle

Question 7

a part of the circle; can be intercepted by angles, chords, secants, and tangents

Answer 7

arc

Question 8

an angle whose vertex is on the circle and whose rays are chords (!) of the circle

Answer 8

inscribed angle

Question 9

an arc forming half a circle

Answer 9

semicircle!

Question 10

an arc measuring LESS than a semicircle (2 LETTERS)

Answer 10

minor arc

Question 11

an arc measuring MORE than a semicircle (3 LETTERS)

Answer 11

major arc

Question 12

circles with the same center but not necessarily the same radius

Answer 12

concentric circles

Question 13

where can a circle be inscribed?

Answer 13

a polygon with each side of the polygon tangent to the circle

Question 14

(x-h)2 + (y-k)2 = r2

Answer 14

center radius form

Question 15

ax2 + bx2 + cx + dy + e = 0

Answer 15

standard form

Question 16

Circle Fact 1

Answer 16

A central angle is = to its intercepted arc (in degrees)

Question 17

Circle Fact 2

Answer 17

An inscribed angle is equal to half its intercepted arc in degrees

Question 18

when given a question listing 2 coordinates on a plane asking for the area of a sector

Answer 18

match up right triangle, find value of x via inverse of tangent and proceed with area sector formula

Question 19

Limit argument (dissection)

Answer 19

the smaller the angle values are of each sector the circle is divided into, the more it resembles a parallelogram

Question 20

Semi circle SA

Answer 20

1/2 pi radius squared

Question 21

Quarter Circle SA

Answer 21

1/4 pi radius squared

Question 22

any sector SA

Answer 22

x/360 pi radius squared

Question 23

Arc length

Answer 23

n/360 pi diameter or n/360 2 pi radius

Question 24

construction for equilateral triangle

Answer 24

1) diameter & plot
2) draw vertical curve after using compass to measure radius
3) connect plots

Question 25

construction for hexagon

Answer 25

1) diameter & plot
2) draw vertical curve after using compass to measure radius
3) connect plots
4) do for both sides

Question 26

construction of a square

Answer 26

1) diameter and plot
2) perp bisect
3) connect plots

Question 27

construction of an octagon

Answer 27

1) diameter and plot
2) perp bisect (4x)
4) connect plots

Question 28

radian measure

Answer 28

radius to degrees - 180 over pi
degrees to radius- pi over 180

Question 29

(x-h)2 + (y-k)2 = r2

Answer 29

circle radius form, convert to standard form via perfect square

Question 30

ax2 + by2 +cx +dy + e = 0

Answer 30

standard form, combine like terms

Question 31

circumference formula

Answer 31

pi(d) or 2pi(r)

Question 32

limit argument for area & circumference

Answer 32

the smaller the angle measure at which each sector is dissected, the more it resembles a parallelogram

1/2 (2 pi r
Radius is height
Base x2 = circumference
1/2 (2pir) (r)
base = 1/2 (2 pi r), simplifies to pi r
plus the radius is pi r2, which is the area of a rectangle

Question 33

Circle Fact 3

Answer 33

An angle formed by a chord and a tangent is equal to half its intercepted arc

Question 34

Circle Fact 4

Answer 34

An angle formed by two chords/two lines intersecting INSIDE a circle is equal to half the SUM of its intercepted arcs

Question 35

Circle Fact 5

Answer 35

An angle formed by any two lines intersecting OUTSIDE of a circle is equal to half the DIFFERENCE of the intercepted arcs

Question 36

Circle Fact 6

Answer 36

If a quadrilateral is inscribed in a circle, the opposite angles are supplementary

Question 37

Circle Fact 7

Answer 37

A radius drawn to the point of tangency is perpendicular to the tangent

Question 38

Circle Fact 8

Answer 38

A radius or diameter perpendicular to a chord bisects the chord and its arcs (and a radius or diameter that bisects a chord is perpendicular to that chord)

Question 39

CIrcle Fact 9

Answer 39

Equal chords intercept equal arcs

Question 40

Circle Fact 10

Answer 40

Parallel chords create congruent arcs

Question 41

Circle Fact 11

Answer 41

Chords equidistant from the center of a circle are congruent

Question 42

Circle Fact 12

Answer 42

Two tangents drawn from the same external point to a circle are congruent

Question 43

Circle Fact 13

Answer 43

If two chords intersect in a circle, the product of their segments is equal (product of parts)
ab = cd

Question 44

Circle Fact 14

Answer 44

If two secants are drawn from the same external point, outside x whole = outside x whole (product of outside and whole)

Question 45

Circle Fact 15

Answer 45

If a secant and tangent are drawn from the same external point, tangent squared = outside x whole
a2 = bc