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Can someone help me with these 2 Euclidean geometry questions?

  • #1
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Poster has been reminded to use the HH Template and show their work

Homework Statement


write the proof

Homework Equations


none

The Attempt at a Solution


I've tried 5 times, got nowhere
 

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Answers and Replies

  • #2
Buzz Bloom
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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
 
  • #3
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What do the numbers (1&2) in the diagram indicate? Are all angles labeled 1 supposed to be equal?
 
  • #4
LCKurtz
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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."
I think it might mean that line SB bisects angle OBC. Here's a picture drawn to scale assuming that:
geometry.jpg
 
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  • #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.
 
  • #6
LCKurtz
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What do the numbers (1&2) in the diagram indicate? Are all angles labeled 1 supposed to be equal?
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.
 
  • #7
LCKurtz
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  • #8
Buzz Bloom
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Buzz, do you have an argument for problem 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.

And I don't see proposition 1.32 at that link. ??
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
 
  • #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.
 
  • #10
haruspex
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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.
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?
 
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  • #11
13
1

Homework Statement


write the proof

Homework Equations


none

The Attempt at a Solution


I've tried 5 times, got nowhere
For the first problem, the theorem which states that equal arcs subtend equal angles on a circle is applicable.
 
  • #12
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Hi guys, thanks a lot for the help. Ive solved both problems. Im going to post the solutions later to this thread. Much appreciated
 
  • #13
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For the first problem, the theorem which states that equal arcs subtend equal angles on a circle is applicable.
I really have to learn geometry. I look foolish with a math degree without knowing geometry
 
  • #14
LCKurtz
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For the first problem, the theorem which states that equal arcs subtend equal angles on a circle is applicable.
You mean like what was mentioned in post #5?
 
  • #15
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You mean like what was mentioned in post #5?
Yes, I see you had already mentioned it.
 

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