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May 25th, 2017, 10:31 AM  #1 
Newbie Joined: May 2017 From: Germany Posts: 5 Thanks: 0  Determine proportion of two lines in a triangle
Hey there. I'm a second semester maths student. I currently have one lecture which I'm not keeping up with because it's a) terrible, it makes me angry, and b) about the topic I'm least interested in, however do still plan to pass the exam this semester, hence why I need help solving this assignment. I think the image is quite selfexplanatory; I need to determine the length of x relative to c. The lower and right line are obviously cut with 2:1 proportion but the third isn't. There is a proof (it probably has some elegant name in English, but I wasn't able to find it) about the centerpoint of a triangle. Here is an image of that one: The proof isn't too difficult and I understand how it works; however I haven't been able to do something similar for my case. Alright, so that's the problem. Any help is greatly appreciated! Last edited by skipjack; May 25th, 2017 at 12:21 PM. 
May 25th, 2017, 12:25 PM  #2 
Global Moderator Joined: Dec 2006 Posts: 17,491 Thanks: 1315 
Have you swapped "2a" and "4a"? Anyway, apply Ceva's theorem.

May 25th, 2017, 10:00 PM  #3  
Newbie Joined: May 2017 From: Germany Posts: 5 Thanks: 0  Quote:
Yeah, that's theorem covers it, now I can certainly get it done. Thanks.  

Tags 
determine, geometry, lines, proportion, triangle 
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