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Two identical touching circles of radius r share the same tangent. A square of side s, rests on the tangent and touches the two circles as shown in the diagram above.  If r is 10 units. Then the side ss of the square is how many units?

 

 Jan 4, 2021
 #1
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See the following  :

 

 

Let C  =(-10,20)     C = (0,0)

 

The slope of  this line =  -2

 

And the  eqation of this  line is   y =   -2x    (1)

 

The equation of the  circle  with its ceenter at  A  is   ( x+10)^2  + ( y - 10)^2  =  100    (2)

 

Sub (1)  into (2)  and we have that

 

(x + 10)^2   + ( -2x - 10)^2  = 100

 

x^2  + 20x + 100  +  4x^2  + 40x + 100    = 100

 

5x^2 + 60x + 100   = 0

 

x^2   + 12x  +  20  =   0     factor as

 

( x  + 10) ( x + 2)   =  0

 

The second factor set to 0   and solved for x  gives  x  = -2 =  x coordinate of F

 

And  the y coordinate is   -2 (-2)    =  4  = HF  =    side of the  square

 

 

 

cool cool cool

 Jan 4, 2021

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