10.1 Circles Flashcards
when we refer to a circle, do we mean the points INSIDE the circle?
NO! we mean the points ON the circle
circle
notation…
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…)
interior of a circle
all the points INSIDE the circle
exterior of a circle
all the points OUTSIDE the circle
chord
a SEGMENT whose endpoints are on the circle
diameter
CHORD that passes through the center of the circle
all diameters of a given circle are…
the common length is called the…
CONGRUENT
THE diameter of the circle (instead of the length of the diameter)
radius (plural form)
(radii)
SEGMENT that has the center as an endpoint AND a point on the circle as the other endpoint
all radii for a given circle are…(and why?)
their common length is called…
CONGRUENT because the definition of a circle
THE radius of the circle (instead of the length of the radius)
2 FORMULAS relating the diameter and the radius of a circle…
D=2r
OR
R=D/2 (R=1/2(D))
what two ways can a LINE INTERSECT a circle?
tangent or secant
tangent
a LINE that intersects a circle at EXACTLY one point
point of tangency
the POINT at which a tangent intersects a circle
secant
alternate definition
a LINE that intersects a circle at TWO points
a LINE that contains a CHORD
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?
NO- it never goes inside the circle
YES- some points are in the interior
common tangent
a line that is tangent to 2 circles
common EXTERNAL tangent
a common tangent that does NOT intersect the SEGMENT that joins the center of the circles
common INTERNAL tangent
a common tangent that DOES intersect the SEGMENT that joins the centers of the circle
2 circles might not intersect AT ALL
what are the three ways this could happen?
- two totally different circles
- they are on different planes
- they are inside each other
2 circles might also intersect
what are the four ways this could happen?
internally tangent circles, externally tangent circles, 2 intersection points, or more than 2 intersection points
tangent circles
circles that have EXACTLY ONE point of intersection
internally tangent circles
NO VENN DIAGRAM
*it’s inside the circle
externally tangent circles
NO VENN DIAGRAM
*it’s outside the circle
2 intersection points
VENN DIAGRAM
*two points
more than 2 intersection points
NO VEN DIAGRAM
*same circle!!!!!! (right on top of each other)
concentric circles
circles that have the same center BUT different radii
congruent circles
two circles are congruent IF AND ONLY IF they have congruent radii OR congruent diameters
concentric circles are ________ congruent circles
NEVER
