2 problems

  • Thread starter recon
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  • #1
399
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?
 

Answers and Replies

  • #2
399
1
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?
 
  • #3
399
1
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.
 
  • #4
VietDao29
Homework Helper
1,424
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Hi,
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
[tex]\frac{41}{42}[/tex]?
Thanks,
Viet Dao,
 
  • #5
399
1
VietDao29 said:
PS: Can you give me the answer for number 1?
Is it
[tex]\frac{41}{42}[/tex]?
Thanks,
Viet Dao,

Thanks for the help. :smile: And yes, that is the answer to question 2, not 1.
 

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