1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Basic geometric proof

  1. Sep 5, 2011 #1
    1. The problem statement, all variables and given/known data

    If O is any point inside a triangle ABC, prove that BA + AC > BO + OC.

    2. Relevant equations



    3. The attempt at a solution

    Any hints? Thanks....
     
  2. jcsd
  3. Sep 5, 2011 #2

    lewando

    User Avatar
    Gold Member

    Since you are looking to prove an inequality, you should consider exploring the (not sure what you call it) Sum of Two Sides of a Triangle is Greater than the Third Side theorem. It also might help to draw a line segment from B through O to a point D on AC.
     
  4. Sep 5, 2011 #3
    AKA "the triangle inequality"
     
  5. Sep 7, 2011 #4
    Still cannot do it... I tried to apply the triangle inequality theorem and extending those lines, but yet, still cannot prove it.

    I am so clueless, I need more hints.. :frown:
     
  6. Sep 7, 2011 #5

    lewando

    User Avatar
    Gold Member

    I thought the hint about extending that line segment would be pretty big. What it does is give you a "bridge" between triangle ABC and BOC. The brigde triangle, BDC, can be related to the other triangles, I guess by using the so-called triangle inequality :uhh:.
     
  7. Sep 7, 2011 #6

    lewando

    User Avatar
    Gold Member

    So try this approach: Do it in steps: first step: only consider BOC and BDC. Write down all the facts you know about this configuration.

    triangle.jpg

    Can you prove this intermediate statement: BD + DC > BO + OC? Try to do this by using the "algebra" of geometry (adding/subtracting the same thing to both sides does not change the truth of the equation/inequality), using your facts to get to the intermediate statement you are trying to prove. Or take the intermediate statement and decompose it into one or more combinations of your facts.

    Good luck. If this wasn't hard, it'd be easy.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Basic geometric proof
  1. Geometric proof. (Replies: 1)

  2. Geometric proof (Replies: 4)

  3. Geometrical Proofs (Replies: 2)

  4. Geometrical Proof (Replies: 6)

Loading...