Online Course Discussion Forum

still need help on p18 in winter camp geometry blue

 
 
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still need help on p18 in winter camp geometry blue
by Iris Xu - Friday, January 15, 2021, 1:08 PM
 

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

 
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Re: still need help on p18 in winter camp geometry blue
by John Lensmire - Saturday, January 16, 2021, 2:02 PM
 

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!

Picture of Iris Xu
Re: still need help on p18 in winter camp geometry blue
by Iris Xu - Sunday, January 17, 2021, 5:07 PM
 

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

Picture of Iris Xu
Re: still need help on p18 in winter camp geometry blue
by Iris Xu - Sunday, January 17, 2021, 6:18 PM
 

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

Picture of Iris Xu
Re: still need help on p18 in winter camp geometry blue
by Iris Xu - Monday, January 18, 2021, 12:18 AM
 

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