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Can anyone help?  I don't know what to do with circles.

 

Two quarter circles of radius 27 are drawn on adjacent corners of a square. A circle is drawn touching these and the bottom side of the square.  Find the radius of this circle.

 

 May 3, 2020
 #1
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If we connect the center  of the smaller circle  with  the center of either larger circle....this distance  = 27 + r

If we draw a segment  from the center of the smaller circle perpendicular to the top edge of the square, this distance  = 54 - r

Lastly....the distance from where this  last segment  meets the top edge of the square to the top right vertex of the square  = 27

 

We  have a right triangle with legs of  54 - r   and 27

And the hypotenuse  = 27 + r

 

So....by the Pythagorean theorem we have that

 

(54 - r)^2 + 27^2  =  (27 + r)^2     simplify

 

2916 - 108r + r^2 + 729  = 729  + 54r + r^2     

 

2916 - 108r    =  54 r 

 

2916  = r (54 + 108)

 

2916  = 162 r     divide both sides by 162

 

18  = r

 

 

cool cool cool

 May 3, 2020

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