Solution 92: A (not necessarily) Trisecting Median

  • Published on May 16, 2019
  • We find the ratio of two cevians by using a property of symmedian and the Stewart's Theorem. Along the way, we also prove the ratio formula for symmedian.
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Comments • 22

  • Prince Ivan
    Prince Ivan 23 days ago

    My solution:
    Let K be on MD s.t. AK bisects

  • adandap
    adandap Month ago +1

    I'll admit I took an engineer's approach to this problem. I applied the cosine rule to every triangle I could find, then found that I had N equations in N unknowns. Therefore the problem was solved in principle. :)

  • VeL0ciTY
    VeL0ciTY Month ago

    Waiting for the physics and Calc ap tests!

    • VeL0ciTY
      VeL0ciTY 29 days ago

      @LetsSolveMathProblems I understand :)

    • LetsSolveMathProblems
      LetsSolveMathProblems  29 days ago

      *Edit: After much debate, I decided to not upload AP FRQ videos for this year, mainly because I believe I cannot post a series of explanation that is of a significantly higher quality than those already posted. If you are interested, turksvids has uploaded all solutions to AP Calculus AB/BC FRQ's from this year:

  • Gabriel Porto
    Gabriel Porto Month ago +4

    Great video. I didn't know about Symmedians, thank you so much. Great explanation as always.

  • Mr5nan
    Mr5nan Month ago +2

    I think I kinda missed something. If you proved that symmedian implies the BD/DC=(AB/AC)^2, don't you have to provide the proof of the other implication as well so that you can say that the angle DAC is theta?

    • Mr5nan
      Mr5nan Month ago

      @LetsSolveMathProblems yeah that would complete the proof 😊

    • LetsSolveMathProblems
      LetsSolveMathProblems  Month ago +5

      Since the foot of the symmedian must be on BC and BD/DC strictly increases as D moves from B to C, it follows that the converse holds as well. In retrospect, I probably should have noted this in the video. I apologize for the possible confusion.

  • Practical Mediocrity

    14:20 you can obtain the result by just considering the large triangle (even though this is not the wisest thing to do).

  • Alberto Zordan
    Alberto Zordan Month ago

    At 1:37 you say for the first of many times in this video a word I can't understand. What is it? "Sedian"? I'm feeling so dumb not being able to grasp this word, maybe I'm not even familiar with what it represents for a triangle. AM is a median to me, whereas AD is not.
    Thanks in advance.

    • Alberto Zordan
      Alberto Zordan Month ago

      @Benjamin Wang Thanks man!

    • Alberto Zordan
      Alberto Zordan Month ago

      @LetsSolveMathProblems I was not even aware of the existence of the word "cevian", let alone its concept, go figure! :D I've never heard of it before, it's already astonishing to me. Now I easily grasp that word, so don't worry about your pronunciation: although it may not be that of a native, it's pretty nice and clear to me :)

    • LetsSolveMathProblems
      LetsSolveMathProblems  Month ago +3

      I was saying "cevian," which is defined to be any segment from a vertex of the triangle to the opposite side. I do acknowledge that my pronunciation is not always clear, so please feel free to comment whenever there is a word you are possibly not familiar with. =)

    • Benjamin Wang
      Benjamin Wang Month ago +4

      Alberto Zordan cevian

  • moroccan geographer
    moroccan geographer Month ago +1

    I am SHOCKED that I was actually able to solve this problem! (I'm 14 by the way)

    • moroccan geographer
      moroccan geographer Month ago

      @LetsSolveMathProblems Thank you so much. By the way I used a completely different method to yours in solving this problem.

    • LetsSolveMathProblems
      LetsSolveMathProblems  Month ago +1

      Kudos to you! I would not been able to solve this problem when I was 14. =)

  • Rohit Chaurasiya
    Rohit Chaurasiya Month ago

    Hey it's 1:54 AM in my country .... Lemme sleep 😝 ......

    • Typo
      Typo Month ago +1

      2:25 AM here

  • Cringe Nae nae baby
    Cringe Nae nae baby Month ago +1

    Your videos make me wish I was good at math. Much love!