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Can someone help me with these 2 Euclidean geometry questions?

  1. Apr 17, 2016 #1
    • Poster has been reminded to use the HH Template and show their work
    1. The problem statement, all variables and given/known data
    write the proof

    2. Relevant equations
    none

    3. The attempt at a solution
    I've tried 5 times, got nowhere
     

    Attached Files:

  2. jcsd
  3. Apr 17, 2016 #2
    Hi Ameer Bux:

    Problem 7 is tricky because the figure is not drawn in a manner consistent with the statements about it. You might find it helpful to redraw it so that SB is a diameter of the circle ABC. At least that's how I interpret the text:"SB bisects ABC."

    Problem 8 is easier. I suggest you look up
    Read about proposition 1.32.

    Hope this helps.

    Regards,
    Buzz
     
  4. Apr 17, 2016 #3
    What do the numbers (1&2) in the diagram indicate? Are all angles labeled 1 supposed to be equal?
     
  5. Apr 17, 2016 #4

    LCKurtz

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    I think it might mean that line SB bisects angle OBC. Here's a picture drawn to scale assuming that:
    geometry.jpg
     
    Last edited: Apr 18, 2016
  6. Apr 18, 2016 #5

    LCKurtz

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    @Ameer Bux I have verified that the figure should look like I drew in the post above with SB bisecting angle ABC. As a hint towards a proof I would remind you that angles on circles that subtend equal arcs are equal.
     
  7. Apr 19, 2016 #6

    LCKurtz

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    Ameer appears to have disappeared, which is annoying enough. But to answer your question, looking at his second picture, I think when he as a 1 and 2 at vertex A that it is a very awkward notation where it would have been much better to call them A1 and A2. Similarly the 1 and 2 at vertex R refer to angles better notated as R1 and R2. So all those 1's and 2's are different. Awful notation in his pictures.
     
  8. Apr 21, 2016 #7

    LCKurtz

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    Buzz, do you have an argument for problem 8? I don't see it and I have my doubts it is even true. And I don't see proposition 1.32 at that link. ??
     
  9. Apr 22, 2016 #8
    Hi LCKurtz:

    Thank you for noting my error. Somehow I read the handwritten question as referring to R1 rather than B1. Sorry for my carelessness. Just another of my senior moments.

    From the link:
    ... the term "exterior angle theorem" has been applied to a different result,[1] namely the portion of Proposition 1.32 which states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the remote interior angles.​

    Regards,
    Buzz

     
  10. Apr 22, 2016 #9

    LCKurtz

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    Hi Buzz. I wasn't trying to point out errors though, I'm really wondering if his Problem 8 is true. So I was hoping you had a proof. I can't figure out a proof and I drew what I consider to be a reasonably accurate figure which leads me to believe it may be false.
     
  11. Apr 23, 2016 #10

    haruspex

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    Maybe I am missing something but it looks quite easy.
    I sent details to Buzz in a private conversation, but for some reason it would not let me add you as a recipient. You must be in a higher astral plane. I thought it premature to post what might be a solution to the thread.

    @Ameer Bux , what do you know about opposite angles of a quadrilateral whose vertices lie on a circle?
     
    Last edited: Apr 23, 2016
  12. Apr 24, 2016 #11
    For the first problem, the theorem which states that equal arcs subtend equal angles on a circle is applicable.
     
  13. Apr 25, 2016 #12
    Hi guys, thanks a lot for the help. Ive solved both problems. Im going to post the solutions later to this thread. Much appreciated
     
  14. Apr 25, 2016 #13
    I really have to learn geometry. I look foolish with a math degree without knowing geometry
     
  15. Apr 25, 2016 #14

    LCKurtz

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    You mean like what was mentioned in post #5?
     
  16. Apr 25, 2016 #15
    Yes, I see you had already mentioned it.
     
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