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![[Post New]](/templates/default/images/icon_minipost_new.gif) 18 Feb 2007 22:40:18 IST
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find the number of ways in which a quadrilateral can be constructed using 8 given line segments of length 1,2,3,4,5,6,7,8 cm (only one of each length) , such that a circle can be inscribed (definitely touching all sides ) in it.
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19 Feb 2007 16:28:32 IST
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IN SUCH TYPE OF QUADS.SOME OF OPPOSITE SIDES IS EQUAL AB+CD=AD+BC NOW NO. OF DIGITS WITH A SUM OF 1=0 NO OF COMBINATIONS=0 ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,2=0 ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,=0 ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,3=1,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,=0 ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,4=1,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,=0 ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,5=2(2,3)(1,4),,,,,,,,,,,,,,,,,,,,,,,,,=2C2=1 DO THIS UPTO A SUM OF 15 BECOZ HIGHEST SUM IS 8+7 ANS =ADDING ALL COMBINATIONS=1+1+3+3+3+3+3+1+1=19
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19 Feb 2007 16:32:27 IST
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IN SUCH TYPE OF QUADS.SOME OF OPPOSITE SIDES IS EQUAL AB+CD=AD+BC NOW NO. OF DIGITS WITH A SUM OF 1=0 NO OF COMBINATIONS=0 ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,2=0 ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,=0 ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,3=1,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,=0 ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,4=1,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,=0 ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,5=2(2,3)(1,4),,,,,,,,,,,,,,,,,,,,,,,,,=2C2=1 DO THIS UPTO A SUM OF 15 BECOZ HIGHEST SUM IS 8+7 ANS =ADDING ALL COMBINATIONS=1+1+3+3+3+3+3+1+1=19
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19 Feb 2007 16:36:54 IST
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IN SUCH TYPE OF QUADS.SOME OF OPPOSITE SIDES IS EQUAL AB+CD=AD+BC NOW NO. OF DIGITS WITH A SUM OF 1=0 NO OF COMBINATIONS=0 ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,2=0 ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,=0 ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,3=1,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,=0 ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,4=1,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,=0 ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,5=2(2,3)(1,4),,,,,,,,,,,,,,,,,,,,,,,,,=2C2=1 DO THIS UPTO A SUM OF 15 BECOZ HIGHEST SUM IS 8+7 ANS =ADDING ALL COMBINATIONS=1+1+3+3+3+3+3+1+1=19
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19 Feb 2007 21:19:38 IST
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well we understood that when you posted that for the first time..
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20 Feb 2007 11:58:33 IST
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thanx 4 d method but ans given is 22
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20 Feb 2007 13:25:41 IST
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how come
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sorry, its =1+1+3+3+6+3+3+1+1=22
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20 Feb 2007 14:26:46 IST
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thanx 4 d ans
check out a new ques I 'll b postin
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20 Feb 2007 19:09:56 IST
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In such type of quadrilaterlas sum of opposite sides are equal.
Hence the no. of ways would be to pick 4 numbers from the given set such that sum of any two numbers would give the sum of the other two and combining them.
Hence the no, of ways = C(2,2)+C(2,2)+C(3,2)+C(3,2)+C(4,2)+C(3,2)+C(3,2)+C(2,2)+C(2,2) = 22
Best Wishes
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Bipin Kumar Dubey
Chemical Dept.
IIT Kharagpur
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22 Feb 2007 12:22:28 IST
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one hat please
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