solution to this geometry question?

[swagmaster420x]

I attempted this for a bit then gave up.
https://gyazo.com/8a6f1301b8261ed42e638ba7dbd014a5

[timothy42b]

Did you draw it on graph paper?

[pencilart3]

The solution is F. Why are you trying to cheat on your homework?

[swagmaster420x]

Did you draw it on graph paper?

No, and that's pointless

[timothy42b]

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. 

[swagmaster420x]

Never mind, it's ez

[swagmaster420x]

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

[theholygideons]

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.

[swagmaster420x]

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. 

[theholygideons]

? 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.

[swagmaster420x]

show me your way, maybe i took an extra step.

Tell me what answer you got 1st

[swagmaster420x]

still waiting for timothy42b  
who says that questions are obvious before he visualizes them

[timothy42b]

still waiting for timothy42b  
who says that questions are obvious before he visualizes them

I do?

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.

[swagmaster420x]

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?

[swagmaster420x]

still waiting for timothy42b 
who says that he doesn't think questions are hard before doing them**.

[jknott]

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.

[swagmaster420x]

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.

[jknott]

fine. i was trying to be helpful but as usual on this puerile forum when that happens you get slagged off.

[swagmaster420x]

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.

[lostinidlewonder]

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.

[swagmaster420x]

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

[jknott]

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.

[swagmaster420x]

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?

[jknott]

Yes, I used the fact that both radii are perpendicular to the tangent so must be the same line.

[swagmaster420x]

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

[rachmaninoff_forever]

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.

[swagmaster420x]

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

[theholygideons]

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.

[swagmaster420x]

Gave the girls some of that D.

Philsophy major