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A small circle inscribed between two indentic big circle. The three circles are also tangent to a line. If the radius of the big circle is 10, find the radius of the small circle

 

 Jan 15, 2021
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We can  form a right triangle with legs of  10-r , 10   and a hypotenuse of 10+ r

 

So we have that

 

(10-r)^2 + 10^2   =  (10 + r)^2       simplify

 

r^2  - 20r  + 100 +  100   =   r^2 + 20r + 100

 

-20r + 200  =  20r + 100

 

100 =  40r

 

r  =  100 / 40  =    5/2  =   2.5

 

 

cool cool cool

 Jan 15, 2021

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