# Area of a sector from a chord

#### 1MileCrash

1. 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.

2. Homework 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

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#### LCKurtz

Homework Helper
Gold Member
It depends on what is allowed "without calculus or trig", but I would say yes.

#### 1MileCrash

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.

#### LCKurtz

Homework Helper
Gold Member
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.

#### 1MileCrash

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.

#### 1MileCrash

We were trolled, no solution.

#### HallsofIvy

Homework Helper
Who was "trolled" and by whom? Where did you get this problem? It's relatively simple to solve but does require trigonometry.

#### 1MileCrash

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.

"Area of a sector from a chord"

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