# area of isosceles triangle given circle radii

Here is a fun little geometry problem. Give it a go if you so desire.

Look at the graph. The radius of the larger circle is 2r and the radius of the smaller circle is r. Find the area of the triangle.

There are many ways to go about it. I used simialr triangles, but perhaps you have a better way.

I just left r=1 in order to graph it. But consider r to be some radius r, not 2 as I have in the graph. The area of the triangle should be expressed in terms of r alone.

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 ebaines Posts: 12,096, Reputation: 1303 Expert #2 Dec 20, 2010, 03:21 PM

I get:

$
Area = 8 \sqrt{8} r^2
$

Similar triangles seems to be the best way.
 galactus Posts: 2,271, Reputation: 282 Ultra Member #3 Dec 20, 2010, 03:33 PM

Yep. That's it.

Except, I expressed it as $16\sqrt{2}r^{2}$.

Same thing.

Cool, ebaines.

This reminds me of the infinite circles inside the triangle, except it stops at 2 circles. :)
 harum Posts: 339, Reputation: 27 Full Member #4 Dec 20, 2010, 04:46 PM
Because FE/GD = 2, CG = FG. I.e. CH = 8r. BH = CH * tan(BCH) = CH * (2/sqrt(32)) = CH/sqrt(8) = r*sqrt(8). S = CH*BH = 16*sqrt(8)*r^2.
 harum Posts: 339, Reputation: 27 Full Member #5 Dec 20, 2010, 09:08 PM
Comment on harum's post
Originally Posted by harum
Because FE/GD = 2, CG = FG. I.e. CH = 8r. BH = CH * tan(BCH) = CH * (2/sqrt(32)) = CH/sqrt(8) = r*sqrt(8). S = CH*BH = 16*sqrt(8)*r^2.
Is there a way to edit a typo? 16*sqrt(2)*r^2
 galactus Posts: 2,271, Reputation: 282 Ultra Member #6 Dec 21, 2010, 02:03 AM

$16sqrt{2}r^{2}$.

As long as no one else has posted afterwards, I have had no trouble editing a post.

You meant $16\sqrt{2}r^{2}$
 harum Posts: 339, Reputation: 27 Full Member #7 Dec 21, 2010, 02:02 PM
Comment on galactus's post
Originally Posted by galactus
$16sqrt{2}r^{2}$.

As long as no one else has posted afterwards, I have had no trouble editing a post.

You meant $16\sqrt{2}r^{2}$
Thanks! 16\sqrt{2}r^{2}
 galactus Posts: 2,271, Reputation: 282 Ultra Member #8 Dec 21, 2010, 02:21 PM

You have to place the tags around your LaTex code.

Math in brackets at the front and /math in brackets when closing
 Unknown008 Posts: 8,076, Reputation: 723 Uber Member #9 Dec 22, 2010, 12:39 PM

And it may sound weird... but the site has got several 'skins' On the one you are on, harum, you can't edit your own post. It's the 'newer skin' and I personally don't like it. You might try the skin made before that, by looking for your settings and look for something about 'Take me back to the old AMHD' or something along those lines. It's been a while I haven't been there myself.

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