10.1 Circles

Question 0

when we refer to a circle, do we mean the points INSIDE the circle?

Answer 0

NO! we mean the points ON the circle

Question 1

circle

notation…

Answer 1

set of all points IN A PLANE that are equidistant from a given point called the CENTER of the circle

will see center: *letter or a circle with a dot in it then a letter (which means circle…)

Question 2

interior of a circle

Answer 2

all the points INSIDE the circle

Question 3

exterior of a circle

Answer 3

all the points OUTSIDE the circle

Question 4

chord

Answer 4

a SEGMENT whose endpoints are on the circle

Question 5

diameter

Answer 5

CHORD that passes through the center of the circle

Question 6

all diameters of a given circle are…

the common length is called the…

Answer 6

CONGRUENT

THE diameter of the circle (instead of the length of the diameter)

Question 7

radius (plural form)

Answer 7

(radii)

SEGMENT that has the center as an endpoint AND a point on the circle as the other endpoint

Question 8

all radii for a given circle are…(and why?)

their common length is called…

Answer 8

CONGRUENT because the definition of a circle

THE radius of the circle (instead of the length of the radius)

Question 9

2 FORMULAS relating the diameter and the radius of a circle…

Answer 9

D=2r
OR
R=D/2 (R=1/2(D))

Question 10

what two ways can a LINE INTERSECT a circle?

Answer 10

tangent or secant

Question 11

tangent

Answer 11

a LINE that intersects a circle at EXACTLY one point

Question 12

point of tangency

Answer 12

the POINT at which a tangent intersects a circle

Question 13

secant

alternate definition

Answer 13

a LINE that intersects a circle at TWO points

a LINE that contains a CHORD

Question 14

can any points on a tangent line to a circle lie in the interior of a circle?
can any points on a secant line to a circle lie in the interior of a circle?

Answer 14

NO- it never goes inside the circle

YES- some points are in the interior

Question 15

common tangent

Answer 15

a line that is tangent to 2 circles

Question 16

common EXTERNAL tangent

Answer 16

a common tangent that does NOT intersect the SEGMENT that joins the center of the circles

Question 17

common INTERNAL tangent

Answer 17

a common tangent that DOES intersect the SEGMENT that joins the centers of the circle

Question 18

2 circles might not intersect AT ALL

what are the three ways this could happen?

Answer 18

1. two totally different circles
2. they are on different planes
3. they are inside each other

Question 19

2 circles might also intersect

what are the four ways this could happen?

Answer 19

internally tangent circles, externally tangent circles, 2 intersection points, or more than 2 intersection points

Question 20

tangent circles

Answer 20

circles that have EXACTLY ONE point of intersection

Question 21

internally tangent circles

Answer 21

NO VENN DIAGRAM

*it’s inside the circle

Question 22

externally tangent circles

Answer 22

NO VENN DIAGRAM

*it’s outside the circle

Question 23

2 intersection points

Answer 23

VENN DIAGRAM

*two points

Question 24

more than 2 intersection points

Answer 24

NO VEN DIAGRAM

*same circle!!!!!! (right on top of each other)

Question 25

concentric circles

Answer 25

circles that have the same center BUT different radii

Question 26

congruent circles

Answer 26

two circles are congruent IF AND ONLY IF they have congruent radii OR congruent diameters

Question 27

concentric circles are ________ congruent circles

Answer 27

NEVER