Finding radii for circles inscribed in a triangle

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Finding radii for circles inscribed in a triangle

Postby jwroblewski44 on Wed Jul 17, 2013 3:13 pm

I have a problem I am working on from a book in a pdf format, so I have a screen capture of the problem. It seems that this forum does not allow me to upload my photo though? I must upload it because it is a diagram that would be difficult for me to describe accurately.

Any ideas on how to post the picture?


On the chance that I absolutely cannot upload my screen cap, I will try to describe the diagram. There is an equilateral triangle who's sides are equal to 16cm that has four circles inside it. There is one large circle that is tangent with the triangle on all three sides. Inside each angle of the triangle is a smaller circle, which is tangent to the large circle at one point and tangent to the triangle at two points. The three small circles are congruent to each other and there is a total of four circles inside the triangle.

My objective is to find the radius of both the large circle and the smaller circles. I have been able to prove that the radius of the large circle is (tan30 * 8), but I'm stuck on how to solve the radius of the smaller circles. I hope the description I gave was sufficient.
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Re: Finding radii for circles inscribed in a triangle

Postby maggiemagnet on Wed Jul 17, 2013 5:18 pm

jwroblewski44 wrote:It seems that this forum does not allow me to upload my photo though?

Maybe because you're a new user? (Blocking links and attachments for the first few posts seems to have cut down on the spam, and especially on the pornographic pictures.) :oops:

jwroblewski44 wrote:There is an equilateral triangle who's sides are equal to 16cm that has four circles inside it. There is one large circle that is tangent with the triangle on all three sides. Inside each angle of the triangle is a smaller circle, which is tangent to the large circle at one point and tangent to the triangle at two points. The three small circles are congruent to each other and there is a total of four circles inside the triangle.

So your picture looks something like the one posted here or here? Thanks!
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Re: Finding radii for circles inscribed in a triangle

Postby jwroblewski44 on Wed Jul 17, 2013 7:20 pm

That's exactly what I was looking for. It's strange to see them using a theory/postulate(?) to solve the solution that I wasn't taught yet.
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Re: Finding radii for circles inscribed in a triangle

Postby maggiemagnet on Wed Jul 17, 2013 9:30 pm

jwroblewski44 wrote:That's exactly what I was looking for. It's strange to see them using a theory/postulate(?) to solve the solution that I wasn't taught yet.

Could you get what you needed from the links, or are you still stuck? Thanks!
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