CPhill

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Nombre de usuarioCPhill
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 #2
avatar+91141 
+3

I agree with X2.....this one is difficult.....!!!

I took an alternative approach....in the interest of space cosiderations, I will use some tecnology to help with the answer....but....I get the same answer as X2 did!!!

 

First of all..... I wanted to find the point  where the tangent line intersects the x axis

Let this point =  A

 

Call  the distance between (2, 0) and A =  x

 

So..  using similar triangles..we have this relationship

 

[ x ] / [ 6 + x]  =  1 / 9

9x  =  6 + x

8x  = 6

x = 6/8  =  3/4

So....the point is  ( 2 - x , 0)  =  ( 2 - 3/4, 0)  =  (1.25, 0)  = A

 

Now we can find the distance betwwen the center of the smaller circle and A by using similar triangles again....call the distance, y....so we have

 

[ 1 + y] / [ 11 + y]  = [ 1 ] / [ 9]

9 [ 1 + y ]  = 11 + y

9 + 9y  = 11 + y

8y = 2

y = 1/4   = .25

 

And we can find the distance  between A  and the point where the tangent line touches the smaller circle  as    sqrt [ (1 + 1/4)^2  - 1]  =  sqrt [ (5/4)^2 - 1]  = sqrt [ (25 -16)/ 16] = sqrt (9/16) =

3/4   = .75

 

And we can find the point where the tangent line touches the smaller circle by using a little technology to find the intersection of these two circles :

(x - 2)^2  + ( y - 1)^2  = 1

(x - 1.25)^2 + y^2  = .75^2      

(1.04, 0.72)  =  B

 

 

Likewise......we can find the distance  between A  and the point where the tangent line touches the larger circle  as    sqrt  [ 11.25^2   - 9^2]  =  6.75

 

And........We can find the point where the tangent line touches the larger circle by using a little technology to find the intersection of these two circles :

(x - 8)^2  + (y - 9)^2  =  81

(x - 1.25)^2 + y^2  = 6.75^2    

( -0.64, 6.48) = C

 

The slope between B and C  is

 

[ 6.48 - 0.72] / [ -0.64 - 1.04)  =  [ 5.76 ] / [-1.68]  = -24/7

 

So....using  A  and this slope we can write an equation of the tangent line as

 

y  = (-24/7)(x - 1.25)

y = (-24/7) (x - 5/4)

y = (-24/7)x + 120/ 28

y = (-24/7)x + 30/ 7

 

So...."b"   =  30/7

 

 

 

cool cool cool

CPhill 10 hours ago
 #3
avatar+91141 
0
CPhill 16-nov-2018 22:06