Geometry Chapter 10 - Properties of Circles Section 10.6 - Find Segment Lengths in Circles What the student should get from this: 1. Find the lengths of segments formed by lines that intersect circles 2. Use the lengths of segments in circles to solve problems First we need to know a couple of things... Whatʼs a tangent? Whatʼs a chord? Whatʼs a secant? Draw each! The next thing to think about... If two chords intersect, the product of the lengths of their segments are equal. Example: d c a b a ! b = c ! d Another example: "#$% & 2.5 2 x 4.2
Transcript
GeometryChapter 10 - Properties of CirclesSection 10.6 - Find Segment Lengths in Circles
What the student should get from this:1. Find the lengths of segments formed by lines that intersect circles2. Use the lengths of segments in circles to solve problems
First we need to know a couple of things...
Whatʼs a tangent?
Whatʼs a chord?
Whatʼs a secant?
Draw each!
The next thing to think about...
If two chords intersect, the product of the lengths of their segments are equal.
Example:
d
c
Another example:
2.5
a
b
2
x 4.2
GeometryChapter 10 - Properties of CirclesSection 10.6 - Find Segment Lengths in Circles
What the student should get from this:1. Find the lengths of segments formed by lines that intersect circles2. Use the lengths of segments in circles to solve problems
First we need to know a couple of things...
Whatʼs a tangent?
Whatʼs a chord?
Whatʼs a secant?
Draw each!
The next thing to think about...
If two chords intersect, the product of the lengths of their segments are equal.
Example:
d
c
Another example:
2.5
a
b
2
x 4.2
! ! ! !!!!!!! !!!!!!!!!!!!!!!!
GeometryChapter 10 - Properties of CirclesSection 10.6 - Find Segment Lengths in Circles
What the student should get from this:1. Find the lengths of segments formed by lines that intersect circles2. Use the lengths of segments in circles to solve problems
First we need to know a couple of things...
Whatʼs a tangent?
Whatʼs a chord?
Whatʼs a secant?
Draw each!
The next thing to think about...
If two chords intersect, the product of the lengths of their segments are equal.
Example:
d
c
Another example:
2.5
a
b
2
x 4.2
!!
GeometryChapter 10 - Properties of CirclesSection 10.6 - Find Segment Lengths in Circles
What the student should get from this:1. Find the lengths of segments formed by lines that intersect circles2. Use the lengths of segments in circles to solve problems
First we need to know a couple of things...
Whatʼs a tangent?
Whatʼs a chord?
Whatʼs a secant?
Draw each!
The next thing to think about...
If two chords intersect, the product of the lengths of their segments are equal.
Example:
d
c
Another example:
2.5
a
b
2
x 4.2
!
Last rule... when secant intersects a tangent of a circle, the square of the tangent segment equals the product of the lengths of the other secant segment and its external segment.
Example:
Another example:
x
12
15
a
c
b
!
GeometryChapter 10 - Properties of CirclesSection 10.6 - Find Segment Lengths in Circles
What the student should get from this:1. Find the lengths of segments formed by lines that intersect circles2. Use the lengths of segments in circles to solve problems
First we need to know a couple of things...
Whatʼs a tangent?
Whatʼs a chord?
Whatʼs a secant?
Draw each!
The next thing to think about...
If two chords intersect, the product of the lengths of their segments are equal.
Example:
d
c
Another example:
2.5
a
b
2
x 4.2a !b = c !d !
GeometryChapter 10 - Properties of CirclesSection 10.6 - Find Segment Lengths in Circles
What the student should get from this:1. Find the lengths of segments formed by lines that intersect circles2. Use the lengths of segments in circles to solve problems
First we need to know a couple of things...
Whatʼs a tangent?
Whatʼs a chord?
Whatʼs a secant?
Draw each!
The next thing to think about...
If two chords intersect, the product of the lengths of their segments are equal.
Example:
d
c
Another example:
2.5
a
b
2
x 4.2
"#$%!&!
! ! ! ! ! !
GeometryChapter 10 - Properties of CirclesSection 10.6 - Find Segment Lengths in Circles
What the student should get from this:1. Find the lengths of segments formed by lines that intersect circles2. Use the lengths of segments in circles to solve problems
First we need to know a couple of things...
Whatʼs a tangent?
Whatʼs a chord?
Whatʼs a secant?
Draw each!
The next thing to think about...
If two chords intersect, the product of the lengths of their segments are equal.
Example:
d
c
Another example:
2.5
a
b
2
x 4.2
!
!
Last rule... when secant intersects a tangent of a circle, the square of the tangent segment equals the product of the lengths of the other secant segment and its external segment.
Example:
Another example:
x
12
15
a
c
b
Another rule... when two secants intersect outside the circle, the product of the lengths of one secant segment and its external secant segment equals the product of the lengths of the other secant segment and its external segment.
Example:
b a
c
d
Another example:
x16
18 5
!
Last rule... when secant intersects a tangent of a circle, the square of the tangent segment equals the product of the lengths of the other secant segment and its external segment.
Example:
Another example:
x
12
15
a
c
b
!
Another rule... when two secants intersect outside the circle, the product of the lengths of one secant segment and its external secant segment equals the product of the lengths of the other secant segment and its external segment.
Example:
b a
c
d
Another example:
x16
18 5
a !(a + b) = c !(c + d) !!!
Another rule... when two secants intersect outside the circle, the product of the lengths of one secant segment and its external secant segment equals the product of the lengths of the other secant segment and its external segment.
Example:
b a
c
d
Another example:
x16
18 5
"#$%!&!
! ! ! !
Another rule... when two secants intersect outside the circle, the product of the lengths of one secant segment and its external secant segment equals the product of the lengths of the other secant segment and its external segment.
Example:
b a
c
d
Another example:
x16
18 5
!Last rule... when secant intersects a tangent of a circle, the square of the tangent segment equals the product of the lengths of the other secant segment and its external segment.
Example:
Another example:
x
12
15
a
c
b
!
Last rule... when secant intersects a tangent of a circle, the square of the tangent segment equals the product of the lengths of the other secant segment and its external segment.
Example:
Another example:
x
12
15
a
c
b
!
Last rule... when secant intersects a tangent of a circle, the square of the tangent segment equals the product of the lengths of the other secant segment and its external segment.
Example:
Another example:
x
12
15
a
c
b
! a2 = b ! b + c( ) !!!!
Example: solve for the variables.
Assignment: p.692 #s 3-20 all, 22. Show work. Draw all pictures. Enjoy! Due next period.
x3.5 in.
2.5 in.
x
12 in.
3 in.
22 in.
12 in.
13.5 in.
x
Find the radius of the circle.
!'(!
Last rule... when secant intersects a tangent of a circle, the square of the tangent segment equals the product of the lengths of the other secant segment and its external segment.
Example:
Another example:
x
12
15
a
c
b
!)(!!
!!!!!!
Example: solve for the variables.
Assignment: p.692 #s 3-20 all, 22. Show work. Draw all pictures. Enjoy! Due next period.
x3.5 in.
2.5 in.
x
12 in.
3 in.
22 in.
12 in.
13.5 in.
x
Find the radius of the circle.
!*(!
Example: solve for the variables.
Assignment: p.692 #s 3-20 all, 22. Show work. Draw all pictures. Enjoy! Due next period.
x3.5 in.
2.5 in.
x
12 in.
3 in.
22 in.
12 in.
13.5 in.
x
Find the radius of the circle.
!
Example: solve for the variables.
Assignment: p.692 #s 3-20 all, 22. Show work. Draw all pictures. Enjoy! Due next period.
x3.5 in.
2.5 in.
x
12 in.
3 in.
22 in.
12 in.
13.5 in.
x
Find the radius of the circle. !
! ! ! ! ! ! ! ! !!!
Example: solve for the variables.
Assignment: p.692 #s 3-20 all, 22. Show work. Draw all pictures. Enjoy! Due next period.
x3.5 in.
2.5 in.
x
12 in.
3 in.
22 in.
12 in.
13.5 in.
x
Find the radius of the circle.
!!
Example: solve for the variables.
Assignment: p.692 #s 3-20 all, 22. Show work. Draw all pictures. Enjoy! Due next period.
