section 10-1 tangents to circles. circle the set of all points in a plane that are equidistant from...

Section 10-1Tangents to

Circles

Circle• The set of all points in a

plane that are equidistant from a given point (center).

CenterCircles are named by their center!

P

Circle P

Interior of a circle• Consists of the points inside

the circle

Exterior of a circle

• Consists of the points outside the circle

L

A

N

G

E

P

Radius

Radius• The distance from the

center of a circle to a point on the circle

P

Radius• Segment whose endpoints are the center of the circle and a point on the circle

• All radii of a circle are congruent!

Two circles are congruent if they have the same

radius.

Chord• A segment whose endpoints

lie on a circle

Diameter• The distance across the

circle, through the center• The diameter is twice the

radius

Diameter

A diameter is a chord of a circle.

Secant• A line that intersects a circle

in two points.–It goes through the circle!

Secant

• A line in the plane of a circle that intersects the circle in exactly one point, called the point of tangency.

tangent

Tangent Line

Point of Tangency

Chord

Diameter

Secant

P

Circle P

Common tangent• A line or segment that is

tangent to two coplanar circles

Common internal tangent

• Intersects the segment that joins the centers of two circles

A

B

Common external tangent• Does NOT intersect the

segment that joins the centers of two circles.

A

B

In a plane, two circles can

intersect in two points, one point,

or no points.

two points of intersection:

One point of intersection:

One point of intersection:

no points of intersection:

Concentric circles• Circles that lie in the same

plane and have the same center