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still need help on p18 in winter camp geometry blue

 
 
XuIris的头像
still need help on p18 in winter camp geometry blue
XuIris - 2021年01月15日 Friday 13:08
 

Could I have more detailed hints on how to find the ratio of BC to CF? thanks

 
LensmireJohn的头像
Re: still need help on p18 in winter camp geometry blue
LensmireJohn - 2021年01月16日 Saturday 14:02
 

Hi Iris. A good place to start is with the center of the circle. Then it can be helpful to connect this to all the relevant points and label everything. An example of how this could go is below:


There's still some work to do here. As some additional hints, try to show the following:

  1. $\triangle OBD\sim\triangle BHD$
  2. $HGCO$ is a cyclic quadrilateral
  3. $\triangle BGH\cong\triangle CGE$
  4. $\triangle CEF\sim\triangle EBF$

Hope this helps a little more!

XuIris的头像
Re: still need help on p18 in winter camp geometry blue
XuIris - 2021年01月17日 Sunday 17:07
 

Thanks, professor. I am still not sure how you get #4 above. also, how to use the condition that CD is an angle bisector?

XuIris的头像
Re: still need help on p18 in winter camp geometry blue
XuIris - 2021年01月17日 Sunday 18:18
 

I also don't know how to prove that HGCOHGCO is a cyclic quadrilateral

XuIris的头像
Re: still need help on p18 in winter camp geometry blue
XuIris - 2021年01月18日 Monday 00:18
 

I was not able to prove  triangle BGH is identical to triangle CGE either