My Math Forum triangle and circle

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 December 21st, 2012, 04:00 PM #1 Senior Member   Joined: Dec 2012 Posts: 148 Thanks: 0 triangle and circle A circle inscribed into a triangle ABC, sides of triangle ABC are a, b & c. The tangent points are D, E, & F. Find the sides of triangle DEF. My answer is $2(u-b)(u-c) \sqrt{ \frac{u-a}{ubc} } \\ \\ 2(u-a)(u-c) \sqrt{ \frac{u-b}{uac} } \\ \\ 2(u-b)(u-a) \sqrt{ \frac{u-c}{uab} } \\ \\ u= \frac{a+b+c}{2}$ Can anyone check this?
 December 21st, 2012, 08:42 PM #2 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,274 Thanks: 1023 Re: triangle and circle DEFINITELY not correct. Try that on ABC = 3-4-5 triangle.
 December 21st, 2012, 09:34 PM #3 Senior Member   Joined: Dec 2012 Posts: 148 Thanks: 0 Re: triangle and circle Ok. Where did I do wrong?
December 22nd, 2012, 02:42 AM   #4
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Re: triangle and circle

Quote:
 Originally Posted by tahir.iman Ok. Where did I do wrong?
Somewhere on the sheet(s) of paper you were using to do your calculations

 December 22nd, 2012, 03:22 AM #5 Senior Member   Joined: Dec 2012 Posts: 148 Thanks: 0 Re: triangle and circle check this $\frac{ 2(u-a) \sqrt{ (u-b)(u-c) } }{ \sqrt{bc} }$ and etc.
 December 22nd, 2012, 11:00 AM #6 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,274 Thanks: 1023 Re: triangle and circle Correct! Did you switch fron cheap Russian vodka to Canadian Club whiskey? Made up program to search for integer cases: only found this primitive case(keeping a<1000): a=350, b=625, c=625 ; area = 105000 d = 210, e=210, f=252 ; area = 21168 My Xmas gift to you
December 23rd, 2012, 05:50 AM   #7
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Re: triangle and circle

Quote:
 Originally Posted by Denis Correct! Did you switch fron cheap Russian vodka to Canadian Club whiskey? Made up program to search for integer cases: only found this primitive case(keeping a<1000): a=350, b=625, c=625 ; area = 105000 d = 210, e=210, f=252 ; area = 21168 My Xmas gift to you
Thanks. And no, I mixed Russian vodka with Irish beer.

December 23rd, 2012, 08:53 AM   #8
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Re: triangle and circle

Quote:
 Originally Posted by tahir.iman And no, I mixed Russian vodka with Irish beer.
Keep that up and you'll have 1 + 1 = 3

December 23rd, 2012, 06:31 PM   #9
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Re: triangle and circle

Quote:
Originally Posted by Denis
Quote:
 Originally Posted by tahir.iman And no, I mixed Russian vodka with Irish beer.
Keep that up and you'll have 1 + 1 = 3
Evangelist monks tell every day, 1+1+1=1, so what they drink, or/and smoke. I hope not red wine with red bull, because I love it, and I don't want to come crazy contradictions.

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