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August 5th, 2012, 03:48 PM  #1 
Member Joined: Jul 2012 Posts: 41 Thanks: 0  prove that ( BIOC) cyclic quadrilaterals
prove that ( BIOC) cyclic quadrilaterals

August 6th, 2012, 09:54 AM  #2 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,581 Thanks: 1038  Re: prove that ( BIOC) cyclic quadrilaterals
Dunno, but I can't "see or understand" your problem; I guess others can't either....since you got no replies... SO....can you clarify 
August 6th, 2012, 01:17 PM  #3 
Senior Member Joined: Jun 2011 Posts: 164 Thanks: 0  Re: prove that ( BIOC) cyclic quadrilaterals
According to your information, the drawing should be something like this, it looks very strange... did I draw something wrong? Please Clarify if I made a mistake so I could try to fix it

August 6th, 2012, 02:53 PM  #4 
Member Joined: Jul 2012 Posts: 41 Thanks: 0  Re: prove that ( BIOC) cyclic quadrilaterals
prove that ( HDBF) cyclic quadrilaterals ANGLE HFG =60 
August 6th, 2012, 02:57 PM  #5  
Member Joined: Jul 2012 Posts: 41 Thanks: 0  Re: prove that ( BIOC) cyclic quadrilaterals Quote:
 
August 6th, 2012, 06:24 PM  #6 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,581 Thanks: 1038  Re: prove that ( BIOC) cyclic quadrilaterals
Angle at HFG = 60?! So an equilateral triangle? I don't need this headache...all yours Mark! 
August 6th, 2012, 06:36 PM  #7 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs  Re: prove that ( BIOC) cyclic quadrilaterals
I looked at this some last night, and did consider the equilateral case, which in fact gives a "degenerate" quadrilateral (a triangle) as the inscribed circle and circumscribed circles will both be centered at the incenter of the triangle. I briefly considered a coordinate geometry method, but decided against it as surely there is a much slicker, more elegant way to go here...which of course made me think of "someone else." I could haul out my copy of Euclid's The Elements, but I am lazy today! 
August 6th, 2012, 09:41 PM  #8 
Global Moderator Joined: Dec 2006 Posts: 20,746 Thanks: 2133  }}}}" /> BIC = 180°  (}}}}" /> ABC + }}}}" /> ACB)/2 = 180°  (180°  60°)/2 = 120° and }}}}" /> BOC = 2}}}}" /> BAC = 120°. Hence BIOC is a cyclic quadrilateral. 
August 7th, 2012, 05:26 AM  #9  
Member Joined: Jul 2012 Posts: 41 Thanks: 0  Re: prove that ( BIOC) cyclic quadrilaterals Quote:
H DOES NOT Equal 60  
August 7th, 2012, 05:50 AM  #10 
Member Joined: Jul 2012 Posts: 41 Thanks: 0  Re: prove that ( BIOC) cyclic quadrilaterals
I need more Explain skipjack please 

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bioc, cyclic, prove, quadrilaterals 
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