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Area of a sector from a chord

  1. Mar 25, 2014 #1
    1. The problem statement, all variables and given/known data

    Suppose we have a circle of radius r, and two points A and B on the circle.

    We want to know the area of the sector cut off by A and B as a function of radius r and AB (the length of SEGMENT AB)

    Without calculus or trig.

    2. Relevant equations



    3. The attempt at a solution

    Part of the question included "is this possible" and after trying for a while, I think not.

    Can I get a confirmation either way?

    Thanks
     
  2. jcsd
  3. Mar 25, 2014 #2

    LCKurtz

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    It depends on what is allowed "without calculus or trig", but I would say yes.
     
  4. Mar 25, 2014 #3
    My issue is that I feel like since the area of the sector involves the center angle - easily a transcendental given some interger AB value, that there isn't a way to get that transcendental without trig.
     
  5. Mar 25, 2014 #4

    LCKurtz

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    Of course, you can argue that you don't even know the circumference formula without calculus, or even have the concept of "area" for a circle. That's why I say it depends on what's allowed. Also, I see that you are given the segment AB, which I took to mean the arc AB. If you mean the length of the chord, then I would be more inclined to say no.
     
  6. Mar 25, 2014 #5
    You're right, I should clarify.

    I am allowed to use "high school geometry."

    I know the area of a circle, I know Pythagorean theorem, I know area of a sector (in terms of radius and central angle) and so on.

    But I could not say anything about the central angle with say, arcsin.
     
  7. Mar 25, 2014 #6
    We were trolled, no solution.
     
  8. Mar 25, 2014 #7

    HallsofIvy

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    Who was "trolled" and by whom? Where did you get this problem? It's relatively simple to solve but does require trigonometry.
     
  9. Mar 25, 2014 #8
    My professor asked if it could be done, and if so, show how, for homework.

    In class he revealed that it can't. So we were "trolled" in that we spent a lot of time on it because we figured that professors don't usually ask these if it really can't be done.
     
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