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BCD and EFG are equilateral triangles, and B, C, D, F, and G lie on the same circle.  Let R_1 be the circumradius of BCD, and let R_2 be the cirucmradius of EFG.  Find R_2/R_1.

 

 Dec 28, 2020
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For simplicity, let  the  circumradius of BCD   = 2 =  R1

 

Then the distance  from the center  of  this triangle  to   its base   =  1

 

Then the circumradius of  EFG  must be   [2  -  1]/2   =1/2  = R2

 

So 

 

R2  /R1    =   (1/2)  / 2   = 1/4 

 

 

cool cool cool

 Dec 28, 2020

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