A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

ganeshie8

  • one year ago

show that \(a+b=c\) where \(a,b,c\) are the perpendicular distances from vertices to a line passing through the centroid of an equilateral triangle as shown :

  • This Question is Closed
  1. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1435678656585:dw|

  2. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    sorry for the bad drawing credit to @dan815

  3. dan815
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1435679062232:dw|

  4. dan815
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    are you sure its true, its seems hard to believe

  5. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Yes it is true, verified with geogebra

  6. dan815
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1435679177952:dw|

  7. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \(a\) and \(b\) need to be on the same side of the line

  8. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1435679309628:dw|

  9. dan815
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    oh here is something

  10. dan815
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    we are dealing with 2 sets of parallel slopes here

  11. TrojanPoem
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Well, c = y sinw , a = y sin ( w - 60) , b = y sin(w +60 ) we have to prove that a + b = c left: a + b = ysin(w-60) + ysin(w+60) = y( sin(w-60)+ sin(w+60)) = y[ sinwcos60 - coswsin60 + sinwcos60 + coswsin60] = y* 2sinwcos60 = ysinw = c

  12. dan815
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1435679496205:dw|

  13. TrojanPoem
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @ganeshie8 , here is the proof. Get the other part from the last question

  14. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    that works @TrojanPoem !

  15. dan815
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    trying to not jump into algebra, wanna see if theres a more pure geometry proof

  16. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    exactly ^ there is a really short proof w/o using trig, and looks you had a good start dan

  17. dan815
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1435679888025:dw|

  18. TrojanPoem
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @ganeshie8 , Like++. Nice animation.

  19. dan815
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    3 sets of similar triangles

  20. dan815
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1435680514378:dw|

  21. dan815
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    with sides a b a+b

  22. dan815
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    hey is the motion like a pendulum?

  23. dan815
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    is that a perfect arc

  24. TrojanPoem
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    is think this is a parallelogram with a triangle inscribed

  25. TrojanPoem
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    |dw:1435680716273:dw|

  26. dan815
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    http://prntscr.com/7n5vrt

  27. TrojanPoem
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    AC // BD. CD//AB

  28. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    wow looks like it, nice imagination dan

  29. dan815
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    kind of neat haha, if this relationship defined a pedulum motion in a roundabout way

  30. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    but it cannot be a circle because the length of that top red segment is changing continuously right

  31. dan815
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    ya thats true, a calculus solution to this might look interesting too, something to look for later

  32. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yes @TrojanPoem

  33. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    let me know if you want me to share my solution because i see now it wont spoil anything as there can be multiple solutions

  34. TrojanPoem
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    You gave up guys ?

  35. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    nope, we have ur solution so including mine, technically i have 2 solutions... that is far from giving up :D

  36. TrojanPoem
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Come check the new problem, I am stuck with it.

  37. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    have you posted it already

  38. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    you're right @dan815 the points do trace circles http://gyazo.com/603ef78cc5a38da14adf431b35db870f

  39. TrojanPoem
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I did. But i think it's invisible

  40. ikram002p
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    *

  41. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.