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August 5th, 2012, 03:48 PM   #1
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prove that ( BIOC) cyclic quadrilaterals

prove that ( BIOC) cyclic quadrilaterals
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August 6th, 2012, 09:54 AM   #2
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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
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August 6th, 2012, 01:17 PM   #3
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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
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August 6th, 2012, 02:53 PM   #4
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Re: prove that ( BIOC) cyclic quadrilaterals

prove that ( HDBF) cyclic quadrilaterals
ANGLE HFG =60
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August 6th, 2012, 02:57 PM   #5
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Re: prove that ( BIOC) cyclic quadrilaterals

Quote:
Originally Posted by wuzhe
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
THAT IS correct
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August 6th, 2012, 06:24 PM   #6
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Re: prove that ( BIOC) cyclic quadrilaterals

Angle at HFG = 60?! So an equilateral triangle?
I don't need this headache...all yours Mark!
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August 6th, 2012, 06:36 PM   #7
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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 in-center 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!
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August 6th, 2012, 09:41 PM   #8
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}}}}" /> BIC = 180 - (}}}}" /> ABC + }}}}" /> ACB)/2 = 180 - (180 - 60)/2 = 120 and }}}}" /> BOC = 2}}}}" /> BAC = 120.
Hence BIOC is a cyclic quadrilateral.
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August 7th, 2012, 05:26 AM   #9
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Re: prove that ( BIOC) cyclic quadrilaterals

Quote:
Originally Posted by Denis
Angle at HFG = 60?! So an equilateral triangle?
I don't need this headache...all yours Mark!
F=60
H DOES NOT Equal 60
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August 7th, 2012, 05:50 AM   #10
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Re: prove that ( BIOC) cyclic quadrilaterals

I need more Explain
skipjack
please
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