Area of a sector from a chord

  • Thread starter 1MileCrash
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  • #1
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Homework Statement



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.

Homework Equations





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
 

Answers and Replies

  • #2
LCKurtz
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It depends on what is allowed "without calculus or trig", but I would say yes.
 
  • #3
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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.
 
  • #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.
 
  • #5
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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.
 
  • #6
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We were trolled, no solution.
 
  • #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.
 
  • #8
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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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