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solution to this geometry question? (Read 1463 times)

Offline swagmaster420x

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solution to this geometry question?
« on: October 26, 2015, 04:29:43 AM »
I attempted this for a bit then gave up.
https://gyazo.com/8a6f1301b8261ed42e638ba7dbd014a5

Offline timothy42b

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Re: solution to this geometry question?
«Reply #1 on: October 26, 2015, 11:57:41 AM »
Did you draw it on graph paper?
Tim

Offline pencilart3

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Re: solution to this geometry question?
«Reply #2 on: October 26, 2015, 06:16:18 PM »
The solution is F. Why are you trying to cheat on your homework?
and....i'm on youtube!
youtube.com/noahjohnsonpiano

Offline swagmaster420x

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Re: solution to this geometry question?
«Reply #3 on: October 26, 2015, 07:02:28 PM »
Did you draw it on graph paper?

No, and that's pointless

Offline timothy42b

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Re: solution to this geometry question?
«Reply #4 on: October 26, 2015, 07:35:25 PM »
No, and that's pointless

Making sure you can visualize it properly is not pointless, though.  I drew a quick sketch, then again on graph paper to be sure I understood it.

It looked really obvious at first glance but that was wrong.  I'll take another look when I have more than a minute to work on it.  I don't think this one is hard. 
Tim

Offline swagmaster420x

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Re: solution to this geometry question?
«Reply #5 on: October 26, 2015, 09:22:22 PM »
Never mind, it's ez

Offline swagmaster420x

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Re: solution to this geometry question?
«Reply #6 on: October 27, 2015, 07:21:45 AM »
Making sure you can visualize it properly is not pointless, though.  I drew a quick sketch, then again on graph paper to be sure I understood it.

It looked really obvious at first glance but that was wrong.  I'll take another look when I have more than a minute to work on it.  I don't think this one is hard. 
did you solve it

Offline theholygideons

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Re: solution to this geometry question?
«Reply #7 on: October 27, 2015, 10:43:29 AM »
I solved it. use the fact that the radius of the inner circle is perpendicular to the circumference of the bigger circles, and draw tangents. It's so easy what, are you even asian, disgrace to the asian race man.

Offline swagmaster420x

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Re: solution to this geometry question?
«Reply #8 on: October 27, 2015, 07:28:02 PM »
I solved it. use the fact that the radius of the inner circle is perpendicular to the circumference of the bigger circles, and draw tangents. It's so easy what, are you even asian, disgrace to the asian race man.
? I know how to do it
Based on your explanation I'm not sure you know how to do it
Discounting the straight line that runs from the center of one circle to the other, you don't need to draw a single tangent.  ::)

Offline theholygideons

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Re: solution to this geometry question?
«Reply #9 on: October 28, 2015, 08:32:16 AM »
? I know how to do it
Based on your explanation I'm not sure you know how to do it
Discounting the straight line that runs from the center of one circle to the other, you don't need to draw a single tangent.  ::)
show me your way, maybe i took an extra step.

Offline swagmaster420x

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Re: solution to this geometry question?
«Reply #10 on: October 28, 2015, 08:45:07 AM »
show me your way, maybe i took an extra step.
Tell me what answer you got 1st

Offline swagmaster420x

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Re: solution to this geometry question?
«Reply #11 on: October 28, 2015, 03:42:33 PM »
still waiting for timothy42b  ::)
who says that questions are obvious before he visualizes them

Offline timothy42b

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Re: solution to this geometry question?
«Reply #12 on: October 28, 2015, 04:30:10 PM »
still waiting for timothy42b  ::)
who says that questions are obvious before he visualizes them

I do?
Quote
It looked really obvious at first glance but that was wrong.

I'm the one who said you have to draw it first, which "somebody" angrily rebutted.
Tim

Offline swagmaster420x

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Re: solution to this geometry question?
«Reply #13 on: October 28, 2015, 05:48:15 PM »
I do?
I'm the one who said you have to draw it first, which "somebody" angrily rebutted.
That's not what you said. You said you had to draw it on graph paper, which is completely unnecessary. In a way it's a crutch. Desiring a decent diagram is reasonable though. Out of curiosity, do you have a math background?

Offline swagmaster420x

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Re: solution to this geometry question?
«Reply #14 on: October 29, 2015, 03:23:50 AM »
still waiting for timothy42b  ::)
who says that he doesn't think questions are hard before doing them**.

Offline jknott

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Re: solution to this geometry question?
«Reply #15 on: October 31, 2015, 08:50:28 AM »
clue - draw the diagram (doesn't need to be on graph paper) to give you some known lengths using a little elementary geometry, then solve it algebraically.

I studied the diagram for ages last night to no avail, then turned it into algebra this morning and the answer popped out easily.


Offline swagmaster420x

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Re: solution to this geometry question?
«Reply #16 on: October 31, 2015, 07:48:35 PM »
clue - draw the diagram (doesn't need to be on graph paper) to give you some known lengths using a little elementary geometry, then solve it algebraically.

I studied the diagram for ages last night to no avail, then turned it into algebra this morning and the answer popped out easily.


I've actually done the problem, and while the algebra is simple, it requires you to use a certain property of circles in order to deduce how certain parts of the diagram line up... From there you draw a simple right triangle on which application of the Pythagorean triangle theorem gives you the answer. I have no clue what you mean by "turned it into algebra the next morning", because the moment you spot the right triangle the algebra screams to be applied.

Offline jknott

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Re: solution to this geometry question?
«Reply #17 on: October 31, 2015, 09:40:45 PM »
fine. i was trying to be helpful but as usual on this puerile forum when that happens you get slagged off.




Offline swagmaster420x

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Re: solution to this geometry question?
«Reply #18 on: November 01, 2015, 02:36:12 AM »
fine. i was trying to be helpful but as usual on this puerile forum when that happens you get slagged off.




I just wanted to know if you did the same thing as me, sorry for being abrasive. Did you get the equation, 5/6 squared + r^2 = (1 - r)^2.

Offline lostinidlewonder

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Re: solution to this geometry question?
«Reply #19 on: November 01, 2015, 08:58:59 AM »
You need to use formulas relating to circles, I'm assuming some arc length ones will help, was like 20 years ago I had to use it lol.
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Offline swagmaster420x

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Re: solution to this geometry question?
«Reply #20 on: November 01, 2015, 09:17:54 AM »
You need to use formulas relating to circles, I'm assuming some arc length ones will help, was like 20 years ago I had to use it lol.
'
Try it and seee if ur right

Offline jknott

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Re: solution to this geometry question?
«Reply #21 on: November 01, 2015, 10:31:51 AM »
I just wanted to know if you did the same thing as me, sorry for being abrasive. Did you get the equation, 5/6 squared + r^2 = (1 - r)^2.

yes i did. the squared terms drop out so it's easy.

There's also a more general formula, which is r = 1/2 b (1 - 1/4 b), where b is the width of the overlap. not looked at cases where original circles differ in size, but where they are same size you always get a smaller circle with rational radius.
You can then go on to find even smaller circles, again with rational radius, using Descartes' formula.

Offline swagmaster420x

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Re: solution to this geometry question?
«Reply #22 on: November 01, 2015, 06:41:15 PM »
yes i did. the squared terms drop out so it's easy.

There's also a more general formula, which is r = 1/2 b (1 - 1/4 b), where b is the width of the overlap. not looked at cases where original circles differ in size, but where they are same size you always get a smaller circle with rational radius.
You can then go on to find even smaller circles, again with rational radius, using Descartes' formula.
The derivation of that formula comes directly from the previous equation, I think.
The thing I found tricky was deducing that the radius of the bigger circle and the radius of the smaller circle from the center of each circle to their tangent point are on the same line. I think you need to use the fact that the tangent line to the bigger circle is the same as the tangent line to the smaller circle at their tangent point. Each radius need be perpendicular to this tangent line, implying they're colinear.

How did you infer this?

Offline jknott

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Re: solution to this geometry question?
«Reply #23 on: November 01, 2015, 09:28:18 PM »
Yes, I used the fact that both radii are perpendicular to the tangent so must be the same line.

Offline swagmaster420x

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Re: solution to this geometry question?
«Reply #24 on: April 27, 2016, 09:35:54 PM »
This thread reminds me of the difference between males and females  ::) the former is much more likely to feign competence at a task by saying it seems easy, and then not being able to produce the answer :)) while the female member completes it ::) ;D

Offline rachmaninoff_forever

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Re: solution to this geometry question?
«Reply #25 on: April 28, 2016, 03:48:35 AM »
The solution is F. Why are you trying to cheat on your homework?

Aye man you gotta do what you gotta do to survive in school.

I remember Freshman and Sophmore year I ran a con game where I would give people my theory homework cause I could blast through everything in a few minutes and they would give me their aural skills or music history homework.
Live large, die large.  Leave a giant coffin.

Offline swagmaster420x

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Re: solution to this geometry question?
«Reply #26 on: April 28, 2016, 05:12:35 AM »
Aye man you gotta do what you gotta do to survive in school.

I remember Freshman and Sophmore year I ran a con game where I would give people my theory homework cause I could blast through everything in a few minutes and they would give me their aural skills or music history homework.
Damn straight hustler

Offline theholygideons

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Re: solution to this geometry question?
«Reply #27 on: April 30, 2016, 09:57:58 PM »
Aye man you gotta do what you gotta do to survive in school.

I remember Freshman and Sophmore year I ran a con game where I would give people my theory homework cause I could blast through everything in a few minutes and they would give me their aural skills or music history homework.
Gave the girls some of that D.

Offline swagmaster420x

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Re: solution to this geometry question?
«Reply #28 on: April 30, 2016, 11:06:58 PM »
Gave the girls some of that D.
Philsophy major