## Circle with 4 tangent circles

Geometric formulae, word problems, theorems and proofs, etc.
Leroy
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### Circle with 4 tangent circles

Hi,
Is it possible to draw a large circle containing 4 smaller tangent circles of equal size, without doing any math? ie. can you find the centres of the smaller circles by somehow drawing intersecting lines?

Here's a diagram:
http://etc.usf.edu/clipart/42900/42919/ ... _42919.htm

Thanks,
Leroy

buddy
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### Re: Circle with 4 tangent circles

Is it possible to draw a large circle containing 4 smaller tangent circles of equal size, without doing any math? ie. can you find the centres of the smaller circles by somehow drawing intersecting lines?
What do you mean by "without doing any math"? Can you not use a compass and straightedge? What have you tried so far? What did the instructions for the homework problem say, exactly? Thanks.

Leroy
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### Re: Circle with 4 tangent circles

Sorry thought it might have been a bit vague. This is not a homework problem, I was just curious about this problem. I saw the image and wondered if I could do it without math, meaning without calculating the length of the radius for example. On this site it is called geometric construction.

https://www.mathsisfun.com/geometry/constructions.html

Yes, I would like to use only a compass and straight edge.

I would like to figure it out, so maybe just a push in the right direction.

Leroy
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### Re: Circle with 4 tangent circles

To be more precise, I'm looking to find the point that would be tangent to the large and small circles, instead of just guessing.

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### Re: Circle with 4 tangent circles

I saw the image and wondered if I could do it without math, meaning without calculating the length of the radius for example.
I don't know if you'd have to "calculate" but you'd probably have to do something measurable (even if it's just "duplicating" lengths with the compass, etc). Geometry is "metry" which is "measuring". Maybe do something based on the picture here:

http://www.artofproblemsolving.com/wiki ... Problem_21
To be more precise, I'm looking to find the point that would be tangent to the large and small circles, instead of just guessing.
Points are coordinates, so this is even more mathematical ("calculating") than just doing the drawing. You'll need to start by establishing a coordinate system, determining the radii, etc, and then maybe even doing some calculus. But at least you've got some messy algebra and coordinate geometry ahead of you.

Leroy
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### Re: Circle with 4 tangent circles

I think I figured it out. I made a triangle with a line perpendicular to a line that passed through the center of the large circle. I then bisected one of the other angles. That intersection gave me the center of the smaller circle. From the center of the smaller circle to the point tangent with the larger circle (along the line that passed through the center of the larger circle) gave me the radius of the smaller circle. Thanks for responding.

Leroy
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### Re: Circle with 4 tangent circles

Here's a diagram of what I did. Sorry the colour isn't great.

http://www.hostpic.org/view.php?filenam ... 570114.jpg