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Need help on p18 in winter camp geometry blue

 
 
XuIris的头像
Need help on p18 in winter camp geometry blue
XuIris - 2021年01月13日 Wednesday 13:35
 

thanks for any hints. 

 
WangDr. Kevin的头像
Re: Need help on p18 in winter camp geometry blue
WangDr. Kevin - 2021年01月13日 Wednesday 15:53
 

P18 is one of the harder problems.  There is a typo in the question (hopefully already corrected, but put here just in case): $G$ in the question should be $F$.  It takes some work, but eventually we want to find the ratio $BF/FC$.

XuIris的头像
Re: Need help on p18 in winter camp geometry blue
XuIris - 2021年01月13日 Wednesday 17:17
 

Could you please give some hints on how to find this ratio? thanks

XuIris的头像
Re: Need help on p18 in winter camp geometry blue
XuIris - 2021年01月14日 Thursday 01:11
 

BTW, I found FBD to be identical as AOB and many similar triangles but still got stuck in finding the ratio.