# Can someone help me with these 2 Euclidean geometry questions?

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1. Apr 17, 2016

### Ameer Bux

• 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

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2. Apr 17, 2016

### Buzz Bloom

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

Hope this helps.

Regards,
Buzz

3. Apr 17, 2016

### mfig

What do the numbers (1&2) in the diagram indicate? Are all angles labeled 1 supposed to be equal?

4. Apr 17, 2016

### LCKurtz

I think it might mean that line SB bisects angle OBC. Here's a picture drawn to scale assuming that:

Last edited: Apr 18, 2016
5. Apr 18, 2016

### LCKurtz

@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. Apr 19, 2016

### LCKurtz

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. Apr 21, 2016

### LCKurtz

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. ??

8. Apr 22, 2016

### Buzz Bloom

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.

... 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. Apr 22, 2016

### LCKurtz

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. Apr 23, 2016

### haruspex

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
11. Apr 24, 2016

### atom jana

For the first problem, the theorem which states that equal arcs subtend equal angles on a circle is applicable.

12. Apr 25, 2016

### Ameer Bux

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. Apr 25, 2016

### ciphone

I really have to learn geometry. I look foolish with a math degree without knowing geometry

14. Apr 25, 2016

### LCKurtz

You mean like what was mentioned in post #5?

15. Apr 25, 2016