Comments on: An isosceles triangle of area 3072 contains 3 non-overlapping circles, each of diameter 30. What is its base? http://www.thearealist.com/triangle-area/an-isosceles-triangle-of-area-3072-contains-3-non-overlapping-circles-each-of-diameter-30-what-is-its-base Mon, 12 Jul 2010 16:54:59 -0400 http://wordpress.org/?v=2.8.4 hourly 1 By: rozeta53 http://www.thearealist.com/triangle-area/an-isosceles-triangle-of-area-3072-contains-3-non-overlapping-circles-each-of-diameter-30-what-is-its-base/comment-page-1#comment-1348 rozeta53 Wed, 25 Nov 2009 23:58:59 +0000 http://www.thearealist.com/triangle-area/an-isosceles-triangle-of-area-3072-contains-3-non-overlapping-circles-each-of-diameter-30-what-is-its-base#comment-1348 The smallest equilateral triangle which is tangent to 3 tangent circles inside of it has a side a=30(1+sqrt(3))~81.961524 and a height h=15(3+sqrt(3))~70.980762. Since 3072=3*2^10 ==> a=85 1/3 and h=72, b=sqrt((a/2)^2+h^2). I will post the drawing with more details tomorrow.<br><b>References : </b><br> The smallest equilateral triangle which is tangent to 3 tangent circles inside of it has a side a=30(1+sqrt(3))~81.961524 and a height h=15(3+sqrt(3))~70.980762.
Since 3072=3*2^10 ==> a=85 1/3 and h=72, b=sqrt((a/2)^2+h^2).

I will post the drawing with more details tomorrow.
References :

]]> By: Elio D http://www.thearealist.com/triangle-area/an-isosceles-triangle-of-area-3072-contains-3-non-overlapping-circles-each-of-diameter-30-what-is-its-base/comment-page-1#comment-1347 Elio D Wed, 25 Nov 2009 23:36:59 +0000 http://www.thearealist.com/triangle-area/an-isosceles-triangle-of-area-3072-contains-3-non-overlapping-circles-each-of-diameter-30-what-is-its-base#comment-1347 From my drawing, I SUSPECT, that the diameter of the top circle, added to the diameter of the two bottom ones is 2/3 of the way up the altitude of the triangle. I say I suspect since I haven't had enough time to prove it. IF that is the case, then the altitude is 90, and so 3072 = (1/2)B(90) which means the base B = 3072/45 = 68.2 and 2/3. I have NO PROOF of this.<br><b>References : </b><br> From my drawing, I SUSPECT, that the diameter of the top circle, added to the diameter of the two bottom ones is 2/3 of the way up the altitude of the triangle. I say I suspect since I haven’t had enough time to prove it. IF that is the case, then the altitude is 90, and so

3072 = (1/2)B(90) which means the base B = 3072/45 = 68.2 and 2/3. I have NO PROOF of this.
References :

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