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18
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A Unit circle has center at (5,0) and second circle with a radius 2 units has its center at (17,0). A common tangent to both circles intersects x-axis at Q(a,0) what is value of a

 
 Jun 3, 2021
 #1
avatar+119772 
+1

We can use  similar  triangles  here

 

Let A  be the  center  of the smaller circle  and B the  center of the  larger circle

 

Let BC  =    radius  of  the larger circle        AD  =  radius of smaller cirlce

 

And  triangles  BCQ   and   ADQ  are similar

 

Let  AB  be  the  distance  between the  circles' centers   =   12

 

And   let   x + 1   the  distance  betwen   A    and  Q

 

We  have  this

 

BQ / BC  =  AQ / AD

 

(12  + 1 + x)  /  2     =     (1 + x)    / 1     simplify

 

13 + x   =  2  (1 + x)

 

13 + x  =  2 + 2x

 

13 -  2   =  x

 

11  =  x

 

Q  =  (a , 0)  =   ( 5 - (1 + x) , 0)  =  ( 5 - (12)  , 0)  =    (-7, 0)

 

 

 

cool cool cool

 
 Jun 3, 2021

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