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Draw a circle and then draw and label the Center A Chord A Radius Secant Diameter PowerPoint PPT Presentation


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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

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Draw a circle and then draw and label the center a chord a radius secant diameter

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

14-2 Tangent Lines to Circles


Draw a circle and then draw and label the center a chord a radius secant diameter

  • The interior of a circle is the set of all points of the 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.

  • P

Interior

Exterior


Draw a circle and then draw and label the center a chord a radius secant diameter

  • A 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 A line perpendicular to a radius at its outer end is tangent to the circle.

First minimum theorem


Draw a circle and then draw and label the center a chord a radius secant diameter

  • Theorem 14-3

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

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r

x

P

x

P

r


Draw a circle and then draw and label the center a chord a radius secant diameter

  • 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.


Draw a circle and then draw and label the center a chord a radius secant diameter

Pg. 455(1,3-10,14)


14 2 day 2 chord theorems

14.2 day 2Chord Theorems


Draw a circle and then draw and label the center a chord a radius secant diameter

  • Theorem 14-4

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

Q

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F

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R


Draw a circle and then draw and label the center a chord a radius secant diameter

  • Theorem 14-5

  • 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

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S

P

Q


Draw a circle and then draw and label the center a chord a radius secant diameter

  • Theorem 14-6

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

r

p?

r


Draw a circle and then draw and label the center a chord a radius secant diameter

  • Corollary 14-6.1

  • No circle contains three different collinear points.

L2

L1

Q

Q

S

P

R


Draw a circle and then draw and label the center a chord a radius secant diameter

  • Circles with congruent radius are called congruent.


Draw a circle and then draw and label the center a chord a radius secant diameter

  • Theorem 14-7

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

A

C

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Q

P

F

G

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D

B


Draw a circle and then draw and label the center a chord a radius secant diameter

  • Theorem 14-8

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

C

A

?

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Q

G

P

F

B

D


Draw a circle and then draw and label the center a chord a radius secant diameter

Theorem 14-9 The Line-Circle Theorem

  • 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


Draw a circle and then draw and label the center a chord a radius secant diameter

Pg. 460(1-3,5,8,9)


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