How do i solve this? Circle w/ center O, points B, C on circumference, B, C, O not collinear

F

Felix_GG

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May 4, 2023
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I tried by myself, but I did't get to anywhere. Here is my attempts:1683270829381.png1683270843413.png

Look only for writings made with black pen.

I do know answers, but i want to know how to get them.

2x/y
x^2/1-x
2√3
8√3
 
A general point: the time it would get you to write your work in a cleaner and more explicit form is probably less than it takes us to decipher it.
Felix_GG said:
That's how i got CB.
Click to expand...

What did you get for CB?

And another question: what is your answer for 2-1, i.e., the length of OA ?
 
blamocur said:
A general point: the time it would get you to write your work in a cleaner and more explicit form is probably less than it takes us to decipher it.


What did you get for CB?

And another question: what is your answer for 2-1, i.e., the length of OA ?
Click to expand...
After CB, I got BA. After that I tried to find OA by Pythagorean theorem, but couldn't. I don't know why.
 
blamocur said:
I don't either since you don't even answer my questions. Looks like I can't be of much help in this mode.
Click to expand...
You say that this is the right way to find AO, am i correct? if that so, i will recheck and try again, i already had tried twice, and answer was always the same. I still looking for answer, i tried to find a video about people solving similar problems, but there seem to be no such video. Please, i would be satisfied just by a small hint.
 
Felix_GG said:
After CB, I got BA. After that I tried to find OA by Pythagorean theorem, but couldn't. I don't know why.
Click to expand...
HOW did you evaluate CB, BA and OA? Please post (share) detailed work. Please define all the variables - explicitly. Use a fresh sheet of paper and dark pen. Please donot write over your mistakes. Cut the mistake out with one-line and write again.

I suggest you put the origin at B. Then you will have BA = x and BO = y. Then continue...

A clean step-by-step presentation of Your work will guide us to help you most effectively.
 
Felix_GG said:
You say that this is the right way to find AO, am i correct?
Click to expand...
I asked you two specific questions, but never got any answers or shown any attempt to get those answers. The questions were intended as hints which you asked for.

If you really need help please post your attempts to answer my questions, and please try to make clean drawings and readable explanations. In my experience making clear drawings and writing down clear (attempts at) answers often helps me to see what I was missing before.
 
blamocur said:
I asked you two specific questions, but never got any answers or shown any attempt to get those answers. The questions were intended as hints which you asked for.

If you really need help please post your attempts to answer my questions, and please try to make clean drawings and readable explanations. In my experience making clear drawings and writing down clear (attempts at) answers often helps me to see what I was missing before.
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Yeah, you are right. That's my mistake. here, i rewrote, if there is still something hard to see, i will make it clear.
The next step should have been taking root of whole equation, but i think nothing good will happen.

1683474095995.png
 
Thank you for a much clearer writeup and drawing. Now some notes/questions:
  • You say "let's find CB", but the problem's statement says that CB = 1
  • One thing, i.e. item 1), at a time: how can you express the length of OA through 'x' and 'y' knowing that AB = 2?
 
blamocur said:
Thank you for a much clearer writeup and drawing. Now some notes/questions:
  • You say "let's find CB", but the problem's statement says that CB = 1
  • One thing, i.e. item 1), at a time: how can you express the length of OA through 'x' and 'y' knowing that AB = 2?
Click to expand...
OH MY GOD. I'm so sorry, i thought that "1 and 2" was reffered to ratio of AB and CB, like: if CB is 4 (cm) then AB is 8 (cm) or AB is 5 (cm) then CB is 2.5 (cm). I didn't pay enough attention to notice, that the talk was about their length! My English is still not that good, so possibly that word just slipped my mind. I will immediately try to redo everything and finaly get the answer by myself.
 
blamocur said:
Thank you for a much clearer writeup and drawing. Now some notes/questions:
  • You say "let's find CB", but the problem's statement says that CB = 1
  • One thing, i.e. item 1), at a time: how can you express the length of OA through 'x' and 'y' knowing that AB = 2?
Click to expand...
Yay, i managed to get two answers, but i have no idea how to get the third and the fourth ones.1683480621486.png

Below the line is my attempt of getting the third answer. Use triangle on right as reference:

Firstly i put the value of "y" in equation of "AO" and tried to think up a solution, but answer won't work out. i don't knoww any other way to find "x" or "y". I tried to use the same bisector theorem but it didn't worked too.
 
Felix_GG said:
Below the line is my attempt of getting the third answer. Use triangle on right as reference:

Firstly i put the value of "y" in equation of "AO" and tried to think up a solution, but answer won't work out. i don't knoww any other way to find "x" or "y". I tried to use the same bisector theorem but it didn't worked too.
Click to expand...
I cannot figure out your equations there, but I agree with your answers for (1) and (2).
You already can express 'y' through 'x', and you have one equation for AO in terms of 'x' and 'y'. But you can get another equation for AO using the fact tat ABO is a right triangle. I believe I've found solutions for 'x' and 'y' by using [imath]u=x+y[/imath] and solving first for 'u', then for 'x' and 'y'. But I have no clue why they want you to get those answers in the form described in (3) -- there might be some specific technique which they taught you and which I am not aware of.
 
blamocur said:
I cannot figure out your equations there, but I agree with your answers for (1) and (2).
You already can express 'y' through 'x', and you have one equation for AO in terms of 'x' and 'y'. But you can get another equation for AO using the fact tat ABO is a right triangle. I believe I've found solutions for 'x' and 'y' by using [imath]u=x+y[/imath] and solving first for 'u', then for 'x' and 'y'. But I have no clue why they want you to get those answers in the form described in (3) -- there might be some specific technique which they taught you and which I am not aware of.
Click to expand...
This actually a trial test of Japanese university entry exam. I'm not a japanese and I also don't understand how to get those answers. I was never taught any technique, that's why I'm seeking for somebody who is familiar with japanese math. But you already was a big big help. I think I will repost this problem, to find somebody to help me.
 
Felix_GG said:
This actually a trial test of Japanese university entry exam. I'm not a japanese and I also don't understand how to get those answers. I was never taught any technique, that's why I'm seeking for somebody who is familiar with japanese math. But you already was a big big help. I think I will repost this problem, to find somebody to help me.
Click to expand...
Can you try solving it for 'x' and 'y' without worrying about the format of (3) ?
P.S. I have no clue about Japanese math, but I suspect they do recognize general rules of algebra :)
 
blamocur said:
Can you try solving it for 'x' and 'y' without worrying about the format of (3) ?
P.S. I have no clue about Japanese math, but I suspect they do recognize general rules of algebra :)
Click to expand...
Sorry, I don't really understand what do you mean. I already found "y", didn't I?
 
Felix_GG said:
Sorry, I don't really understand what do you mean. I already found "y", didn't I?
Click to expand...
Do you mean expressing 'y' through 'x' ? That would not be enough since (3) wants you to find solutions for both 'x' and 'y', not just a dependency between them. Or did I miss it somehow?
 
Felix_GG said:
Yay, i managed to get two answers, but i have no idea how to get the third and the fourth ones.View attachment 35747

Below the line is my attempt of getting the third answer. Use triangle on right as reference:

Firstly i put the value of "y" in equation of "AO" and tried to think up a solution, but answer won't work out. i don't knoww any other way to find "x" or "y". I tried to use the same bisector theorem but it didn't worked too.
Click to expand...
It appears that you are using the right triangle shown, but assuming that a + b = c rather than a^2 + b^2 = c^2, the Pythagorean Theorem.

Correct that, and you should be able to solve for x:

1683563666402.png​

I'd simplify before squaring.
 
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