Math Is Fun Forum
  Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

Login

Username

Password

Not registered yet?

#1 2012-03-05 02:08:46

bobbym
Administrator

Offline

Area above a chord.

Hi;

http://www.mathisfunforum.com/showimage.php?pid=203090&filename=jjj.png&preview=true

The question is to find the shaded area between the rectangle and the top part of the circle.

Let's see if Geogebra can help.

1)Draw 4 points (0,0),(0,.53)(1.53,.53)(1.53,0) and call them A,B,C and D.

2)Draw point E at (.765, .35)

3)Use the circle through 3 points tool and draw a circle through A,E and D

4)Draw a line through E and perpendicular to the x axis.

5)Find the point of intersection between the perpendicular line and the circle. Call the bottom point H.

6)Find the midpoint between E and H and call it I. This is the midpoint of the circle.

7)Measure IH with the measuring tool. That is the radius of the circle. You should get 1.01104

8)Measure the angle DIA with the angle tool, you should get 98.33948 degrees.

Now we can use the area above a chord formula



Plugging in r = 1.01104 and θ = 98.33948  we get 0.37153. Now we subtract from .8109 - 0.37153 = 0.439369, which is close. See the drawing to check yours.


Uploaded Images
View Image: 2012-03-04_073024.png      


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#2 2012-03-05 02:13:44

anonimnystefy
Real Member

Offline

Re: Area above a chord.

Hi bobbym

I don't think that's a semicircle.


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#3 2012-03-05 02:34:16

bobbym
Administrator

Offline

Re: Area above a chord.

Hi;

Yes, I know I have corrected it, thanks.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Board footer

Powered by FluxBB