rob_in_1's blog

By rob_in_1, history, 22 months ago, In English,

Can we always form a cyclic quadrilateral using 4 side lengths? I was solving this problem on SPOJ http://www.spoj.com/problems/QUADAREA/. In order to find the maximum area of quadrilateral with side lengths given, I applied Brahmagupta's formula K={\sqrt {(s-a)(s-b)(s-c)(s-d)}}\, and i got AC. I am wondering, is that always possible? Is there any proof?

 
 
 
 
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22 months ago, # |
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Yes.

link

If you choose as an angle between a and d you choose as an angle between b and c, then you have cyclic quadrilateral.

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    22 months ago, # ^ |
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    link

    using this, you can prove that it will be valid quadrilateral by finding diagonal using a and d and using b and c

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    22 months ago, # ^ |
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    But u can control only one angle at a time I guess, either between a and d or between b and c, provided a and d, b and c are adjacent.

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      22 months ago, # ^ |
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      Yes, if you control an angle between a and d, then you know one diagonal, so then you can find an angle between b and c.

      If you choose as an angel between a and d then the angle between b and c is .