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Draw a circle and then draw and label the Center A Chord A Radius Secant Diameter Concentric circle Tangent line. 14-2 Tangent Lines to Circles.

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Draw a circle and then draw and label the

Center

A Chord

A Radius

Secant

Diameter

Concentric circle

Tangent line



  • P

Interior

Exterior


  • A plane whose distance from the center is less than the radius. The exterior of a circle is the set of all points of the plane whose distance from the center is greater than the radius. tangent to a circle is a line (in the same plane) which intersects the circle in one and only one point. This point is called the point of tangency, or point of contact. We say that the line and the circle are tangent at this point.

r

P


Theorem 14 2 a line perpendicular to a radius at its outer end is tangent to the circle
Theorem 14-2 plane whose distance from the center is less than the radius. The exterior of a circle is the set of all points of the plane whose distance from the center is greater than the radius. A line perpendicular to a radius at its outer end is tangent to the circle.

First minimum theorem


  • Theorem 14-3 plane whose distance from the center is less than the radius. The exterior of a circle is the set of all points of the plane whose distance from the center is greater than the radius.

  • Every tangent to a circle is perpendicular to the radius drawn to the point of contact.

?

?

r

x

P

x

P

r


  • Two circles are tangent if they are tangent to the same line at the same point. If two tangent circles are coplanar, and their centers are on the same side of their common tangent, then they are internally tangent. If two tangent circles are coplanar, and their centers are on opposite sides of their common tangent, then they are externally tangent.


Pg. 455(1,3-10,14) at the same point. If two tangent circles are coplanar, and their centers are on the same side of their common tangent, then they are


14 2 day 2 chord theorems
14.2 day 2 at the same point. If two tangent circles are coplanar, and their centers are on the same side of their common tangent, then they are Chord Theorems


  • Theorem 14-4 at the same point. If two tangent circles are coplanar, and their centers are on the same side of their common tangent, then they are

  • The perpendicular from the center of a circle to a chord bisects the chord.

Q

?

P

F

?

R


  • Theorem 14-5 at the same point. If two tangent circles are coplanar, and their centers are on the same side of their common tangent, then they are

  • The segment from the center of a circle to the midpoint of a chord (which is not a diameter) is perpendicular to the chord.

R

?

S

P

Q


  • Theorem 14-6 at the same point. If two tangent circles are coplanar, and their centers are on the same side of their common tangent, then they are

  • In the plane of a circle, the perpendicular bisector of a chord passes through the center.

r

p?

r


  • Corollary 14-6.1 at the same point. If two tangent circles are coplanar, and their centers are on the same side of their common tangent, then they are

  • No circle contains three different collinear points.

L2

L1

Q

Q

S

P

R



  • Theorem 14-7 at the same point. If two tangent circles are coplanar, and their centers are on the same side of their common tangent, then they are

  • In the same circle or in congruent circles, chords equidistant from the center are congruent.

A

C

?

?

Q

P

F

G

?

?

D

B


  • Theorem 14-8 at the same point. If two tangent circles are coplanar, and their centers are on the same side of their common tangent, then they are

  • In the same circle or in congruent circles, any two congruent chords are equidistant from the center.

C

A

?

?

Q

G

P

F

B

D


Theorem 14-9 The Line-Circle Theorem at the same point. If two tangent circles are coplanar, and their centers are on the same side of their common tangent, then they are

  • If a line and a circle are coplanar, and the line intersects the interior of the circle, then it intersects the circle in two and only two points.

X?

r

P

F

s

R

r

X?

L


Pg. 460(1-3,5,8,9) at the same point. If two tangent circles are coplanar, and their centers are on the same side of their common tangent, then they are


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