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2 problems

  1. Jan 10, 2005 #1
    I need to know the names of theorems related to the following two problems:

    1. What is the maximum sum less than 1 but more than 0 that can be formed from [tex]\frac{1}{p} + \frac{1}{q} + \frac{1}{r}[/tex], where p, q and r are positive integers?

    2. What is the maximum perimeter and area of an inscribed quadrilateral and triangle in a circle with a fixed radius r?
  2. jcsd
  3. Jan 10, 2005 #2
    I realise that there may be no established theorems for the above 2 problems, so can anyone please suggest how I can go about solving them?
  4. Jan 11, 2005 #3
    OK, I'm going to shamelessly bump this. *BUMP*

    Can someone tell me if it is even possible to solve the second problem? The first one has been solved already.
  5. Jan 12, 2005 #4


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    Homework Helper

    I am trying to find the maximum perimeter an inscribed quadrilateral, but I haven't succeeded yet.
    About the maximum area an inscribed quadrilateral, I suggest you using:
    [tex]S_{ABC} = \frac{1}{2} \times AB \times AC \times \sin{BAC}[/tex]
    Call A, B, C, D the points on the circle.
    Try to figure out the [tex]S_{AOB}, S_{BOC}, S_{COD}, S_{DOA}[/tex] using the above function.
    OA = OB = OC = OD = R
    And [tex]\sin{90} = 1 \mbox{is max}[/tex]
    So an inscribed quadrilateral has the max erea is the inscribed square.
    That's it.
    Hope it help, :smile:
    PS: Can you give me the answer for number 1?
    Is it
    Viet Dao,
  6. Jan 12, 2005 #5
    Thanks for the help. :smile: And yes, that is the answer to question 2, not 1.
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